The structure of a finite simple group and prime graphs

点击翻译按钮获取中文摘要

We studied about the structure of finite simple groups and found several properties of finite groups using the classification of finite simple groups and prime graphs.Hiroyoshi Yamaki proved that if G is a group of even order and is not 2-rank 1, then there exists an involution t in G such that the order G is bounded by the cube of the order of the centralizer t in G.Yutaka Hiramine studied about difference and relative difference sets for non- abelian groups. Especially Hiramine proved that there exists exactly two relative difference sets in the alternating group on 5 letters. Further more Hiramine constructed relative difference sets in dihedral groups.Naoki Chigira, Masaaki Kitazume and Masaaki Harada constructed self dual code such that the 2^<nd> Janko group acts as automorphism group. Naoki Chigira gave an elementary construction of the Mathieu groups on 11 and 12 letters.Nobuo Iiyori studied prime graphs and solvable graphs of finite groups and defined Burn side ring. Using these it has been proved that we can describe on the connectedness of the solvable graph by the properties of ideals on Burnside ring.Masato Sawabe proved that the reduced Lefschetz module of the G-poset consisting of all centric p-radical subgroups of a finite group G is X-projective virtual Zp[G]-module where X is a family of p-subgroups of the normalizers of non-centric p-radical subgroups of G.