Abstract: Provided is a propylene polymer composition capable of implementing a molded article containing excellent impact resistance. Provided is a propylene polymer composition containing components (A) to (C), satisfying all of requirements (1) to (5), (A) a propylene polymer containing 90 wt % or more of a propylene structural unit; (B) an ethylene-?-olefin copolymer or hydrogenated conjugated diene polymer containing more than 10 wt % and 99 wt % or less of an ethylene structural unit; (C) a propylene block copolymer or graft copolymer containing a propylene polymer segment and an ethylene-?-olefin copolymer segment or a hydrogenated conjugated diene polymer segment; (1) an intrinsic viscosity being 0.5 dl/g or more; (2) CXIS having a number average molecular weight of 40,000 or more; (3) a ratio of the number average molecular weight of CXIS to a number average molecular weight of CXS being 0.

Abstract: A modified solid polyalkylaluminoxane is provided, which is capable of providing ?-olefin suppressing adhesion of any polymer produced as a by-product onto the reactor wall and the stirrer, and which is capable of providing a highly active olefin oligomerization reaction catalyst. An olefin oligomerization reaction catalyst containing the modified solid polyalkylaluminoxane is also provided. The modified solid polyalkylaluminoxane for olefin oligomerization reactions contains structural units represented by general formula (a) and structural units represented by general formula (b), whose median diameter is equal to or larger than 0.1 ?m and equal to or smaller than 50 ?m, in which R? in the general formula (a) represents an alkyl group having 1 to 20 carbon atoms, and R? in the general formula (b) represents a halogenated alkoxy group having 1 to 20 carbon atoms or a halogenated aryloxy group having 6 to 20 carbon atoms.