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In mathematical group theory, a C-group is a group such that the centralizer of any involution has a normal Sylow 2-subgroup. They include as special cases CIT-groups where the centralizer of any involution is a 2-group, and TI-groups where any Sylow 2-subgroups have trivial intersection. The simple C-groups were determined by , and his classification is summarized by . The classification of C-groups was used in Thompson's classification of N-groups. The simple C-groups are *the projective special linear groups PSL2(''p'') for ''p'' a Fermat or Mersenne prime *the projective special linear groups PSL2(9) *the projective special linear groups PSL2(2''n'') for ''n''≥2 *the projective special linear groups PSL3(''q'') for ''q'' a prime power *the Suzuki groups Sz(2''2n+1'') for ''n''≥1 *the projective unitary groups PU3(''q'') for ''q'' a prime power ==CIT-groups== The C-groups include as special cases the CIT-groups, that are groups in which the centralizer of any involution is a 2-group. These were classified by , and the simple ones consist of the C-groups other than PU3(''q'') and PSL3(''q''). The ones whose Sylow 2-subgroups are elementary abelian were classified in a paper of , which was forgotten for many years until rediscovered by Feit in 1970. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「C-group」の詳細全文を読む スポンサード リンク
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