Olefin polymer, olefin polymerization catalyst and process for producing olefin polymer

An olefin polymerization catalyst obtained by contacting:

• a transition metal compound (A) represented by the general formula (1) described below;
• an organoaluminumoxy compound (B) soluble in an aromatic solvent;
• and
• water (C), wherein the molar ratio of aluminum atom contained in the organoaluminumoxy compound (B) to a transition metal atom contained in the transition metal compound (A) is 1 to 20000, and the amount of water used is 0.1 to 3.0 mol per 1 mol of aluminum atom contained in the organoaluminumoxy compound (B),
• wherein M represents a transition metal atom of the Fourth Group of the Periodic Table, X and Y independently represent a hydrogen atom, a halogen atom, an alkyl group, an aryl group, an aralkyl group, an alkoxy group, an aryloxy group, an aralkyloxy group, a sulfonyloxy group, a di-substituted amino group or a substituted silyl group, R1, R2, R3, R4, R5, R6, R7 and R8 independently represent a hydrogen atom, an alkyl group, an aryl group, an aralkyl group, an alkoxy group, an aryloxy group, an aralkyloxy group, a di-substituted amino group or a substituted silyl group, R1, R2, R3, R4, R5, R6, R7 and R8 may be optionally bonded to form a ring, T represents a divalent covalent crosslinking group having 1 to 20 carbon atoms, or a divalent group represented by —O—, —S—, —S—S—, —S(═O)—, —S(═O)2—, —C(═O)—, —N(R9)—, —P(R9)— or —P(═O) (R9)—wherein R9 represents a hydrogen atom or a hydrocarbon group having 1 to 6 carbon atoms in each case, and n is an integer of from 0 to 3.