A method for the prophylaxis of diabetes, diabetic complications, insulin resistance syndrome, metabolic syndrome, hyperglycemia, dyslipidemia, atherosclerosis, cardiac failure, cardiomyopathy, myocardial ischemia, brain ischemia, cerebral apoplexy, pulmonary hypertension, hyperlactacidcemia, mitochondrial disease, mitochondrial encephalomyopathy or cancer in a mammal, comprising administering to the mammal a pharmaceutically effective amount of a compound [I] or a pharmaceutically acceptable salt thereof:
- wherein:
- Ra is:
- (1) a hydrogen atom, or
- (2) a halogen atom;
- Rb is:
- (1) a hydrogen atom,
- (2) a halogen atom,
- (3) a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from a group A,
- (4) a C2-6 alkenyl group optionally substituted by the same or different 1 to 5 substituents selected from a group C,
- (5) a C2-6 alkynyl group optionally substituted by the same or different 1 to 5 substituents selected from the group C,
- (6) a cyano group,
- (7) —C(═O)—Rb1, wherein Rb1 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from a group B,
- (8) —C(═O)—ORb2, wherein Rb2 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (9) —C(═O)—NRb3Rb4, wherein Rb3 and Rb4 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (10) —C(═O)—NRb5—ORb6, wherein Rb5 and Rb6 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (11) —ORb7, wherein Rb7 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (12) —NRb8Rb9, wherein Rb8 and Rb9 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (13) —NRb10—C(═O)—Rb11, wherein Rb10 and Rb11 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (14) —NRb12—C(═O)—ORb13, wherein Rb12 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the following group, and Rb13 is a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (15) —O—C(═O)—NRb14Rb15, wherein Rb14 and Rb15 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B, or
- (16) a group represented by formula:
- wherein:
- Yb is:
- (i) a single bond,
- (ii) a C1-6 alkylene,
- (iii) a C2-6 alkenylene,
- (iv) —O—(CH2)n1—, wherein n1 is an integer of 0, or 1 to 4,
- (v) —O—(CH2)n2—C(═O)—, wherein n2 is an integer of 0, or 1 to 4,
- (vi) —C(═O)—, or
- (vii) —NRb16—, wherein Rb16 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B;
- ring T is:
- (i) a C6-10 aryl group,
- (ii) a C3-10 cycloalkyl group,
- (iii) a C5-10 bridged cycloalkyl group,
- (iv) a monocyclic aromatic heterocyclic group which contains, besides carbon atom, 1 to 4 hetero atoms selected from a nitrogen atom, an oxygen atom and a sulfur atom, and has 3 to 7 ring-constituting atoms, or
- (v) a monocyclic non-aromatic heterocyclic group which contains, besides carbon atom, 1 to 4 hetero atoms selected from a nitrogen atom, an oxygen atom and a sulfur atom, and has 3 to 7 ring-constituting atoms,
- Rj are the same or different and each is a substituent selected from a group D, and p is an integer of 0, or 1 to 4;
- Rc is:
- (1) a hydrogen atom,
- (2) a halogen atom,
- (3) a C1-6 alkyl group,
- (4) —C(═O)—ORc1, wherein Rc1 is a hydrogen atom or a C1-6 alkyl group,
- (5) —ORc2, wherein Rc2 is a hydrogen atom or a C1-6 alkyl group,
- (6) —NRC3Rc4, wherein RC3 and Rc4 are the same or different and each is a hydrogen atom or a C1-6 alkyl group, or
- (7) —NRc5—C(═O)—Rc6, wherein Rc5 and Rc6 are the same or different and each is a hydrogen atom or a C1-6 alkyl group;
- Xd is:
- a nitrogen atom;
- Re are the same or different and each is:
- (1) a halogen atom, or
- (2) a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group C;
- and
- n is an integer of 0, or 1 to 3,
- wherein the Group A is selected from the group consisting of:
- (a) a halogen atom,
- (b) a cyano group,
- (c) —C(═O)—RA1, wherein RA1 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (d) —C(═O)—ORA2, wherein RA2 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (e) —C(═O)—NRA3RA4, wherein RA3 and RA4 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (f) —C(═O)—NRA5—ORA6, wherein RA5 and RA6 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (g) —ORA7, wherein RA7 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the following group B,
- (h) —NRA8RA9, wherein RA8 and RA9 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (i) —NRA10—C(═O)—RA11, wherein RA10 and RA11 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (j) —NRA12—C(═O)—ORA13, wherein RA12 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the following group B, and RA13 is a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (k) —S(═O)2—RA14, wherein RA14 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B,
- (l) —S(═O)2—ORA15, wherein RA15 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group B, and
- (m) —Si—(CH2—CH3)3,
- wherein the Group B is selected from the group consisting of:
- (a) a halogen atom,
- (b) a cyano group,
- (c) —C(═O)—RB1, wherein RB1 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group C,
- (d) —C(═O)—ORB2, wherein RB2 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group C,
- (e) —C(═O)—NRB3RB4, wherein RB3 and RB4 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the following group C,
- (f) —C(═O)—NRB5—ORB6, wherein RB5 and RB6 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group C,
- (g) —ORB7 wherein RB7, is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group C,
- (h) —NRB8RB9, wherein RB8 and RB9 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group C,
- (i) —NRB10—C(═O)—RB11, wherein RB10 and RB11 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group C,
- (j) —NRB12—S(═O)2—RB3, wherein RB12 and RB13 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group C,
- (k) —NRB14—C(═O)—ORB5, wherein RB14 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the following group C, and RB15 is a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group C,
- (l) —S(═O)2—RB6, wherein RB16 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group C, and
- (m) —S(═O)2—ORB17, wherein RB17 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group C,
- wherein the Group C is selected from the group consisting of:
- (a) a halogen atom,
- (b) —C(═O)—RC1, wherein RC1 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 halogen atoms,
- (c) —C(═O)—ORC2, wherein RC2 is a hydrogen atom or a C1-6 alkyl group, and
- (d) —ORC3, wherein RC3 is a hydrogen atom or a C1-6 alkyl group,
- wherein the Group D is selected from the group consisting of:
- (a) a halogen atom,
- (b) a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from a group E,
- (c) a C1-6 alkyl group substituted by a C6-10 aryl group optionally substituted by the same or different 1 to 5 substituents selected from a group F,
- (d) a C1-6 alkyl group substituted by a C3-10 cycloalkyl optionally substituted by the same or different 1 to 5 substituents selected from the group F,
- (e) a C1-6 alkyl group substituted by a C5-10 bridged cycloalkyl optionally substituted by the same or different 1 to 5 substituents selected from the group F,
- (f) a C1-6 alkyl group substituted by a monocyclic aromatic heterocyclic group optionally substituted by the same or different 1 to 5 C1-6 alkyl groups, the monocyclic aromatic heterocyclic group containing 1 to 4 hetero atoms selected from a nitrogen atom, an oxygen atom and a sulfur atom, and has 3 to 7 ring-constituting atoms,
- (g) a C3-10 cycloalkyl group optionally substituted by the same or different 1 to 5 substituents selected from a group F,
- (h) a C5-10 bridged cycloalkyl group optionally substituted by the same or different 1 to 5 substituents selected from group F,
- (i) a cyano group,
- (j) —C(═O)—RD1, wherein RD1 is a hydrogen atom, a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group E, or a monocyclic non-aromatic heterocyclic group optionally substituted by the same or different 1 to 5 substituents selected from the group F, the monocyclic non-aromatic heterocyclic group containing 1 to 4 hetero atoms selected from a nitrogen atom, an oxygen atom and a sulfur atom, and has 3 to 7 ring-constituting atoms,
- (k) —C(═O)—ORD2, wherein RD2 is a hydrogen atom, or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group E,
- (l) —C(═O)—NRD3RD4, wherein RD3 and RD4 are the same or different and each is a hydrogen atom, or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group E,
- (m) —C(═O)—NRD5—ORD6, wherein RD5 and RD6 are the same or different and each is a hydrogen atom, or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group E,
- (n) —ORD7, wherein RD7 is a hydrogen atom, or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group E,
- (o) —NRD8RD9, wherein RD8 and RD9 are the same or different and each is a hydrogen atom, or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group E,
- (p) —NRD10—C(═O)—RD11, wherein RD10 and RD11 are the same or different and each is a hydrogen atom, or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group E,
- (q) —NRD12—C(═O)—ORD13, wherein RD12 is a hydrogen atom, or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group E, and RD13 is a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group E,
- (r) —S(═O)2—RD14, wherein RD14 is a hydrogen atom, or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group E, and
- (s) —S(═O)2—ORD15, wherein RD15 is a hydrogen atom, or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group E,
- wherein the Group E is selected from the group consisting of:
- (a) a halogen atom,
- (b) a cyano group,
- (c) —C(═O)—RE1, wherein RE1 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group F,
- (d) —C(═O)—ORE2, wherein RE2 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group F,
- (e) —C(═O)—NRE3RE4, wherein RE3 and RE4 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group F,
- (f) —C(═O)—NRE5—ORE6, wherein RE5 and RE6 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group F,
- (g) —ORE7, wherein RE7 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group F,
- (h) —NRE8RE9, wherein RE8 and RE9 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group F,
- (i) —NRE10—C(═O)—RE11, wherein RE10 and RE11 are the same or different and each is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group F,
- (j) —NRE12—C(═O)—ORE13, wherein RE12 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the following group F, and RE13 is a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group F,
- (k) —S(═O)2RE14, wherein RE14 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group F,
- (l) —S(═O)2—ORE15, wherein RE15 is a hydrogen atom or a C1-6 alkyl group optionally substituted by the same or different 1 to 5 substituents selected from the group F, and
- (m) —NRE16—S(═O)2—RE17, wherein RE16 and RE17 are the same or different and each is a hydrogen atom or a C1-6 alkyl group, and
- wherein the Group F is selected from the group consisting of:
- (a) —(CH2)nF1—C(═O)—ORF1, wherein RF1 is a hydrogen atom or a C1-6 alkyl group, and nF1 is an integer of 0, or 1 to 4, and
- (b) —(CH2)nF2—ORF2, wherein RF2 is a hydrogen atom or a C1-6 alkyl group, and nF2 is an integer of 0, or 1 to 4.