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(2n) for n≥2 the projective special linear groups PSL3(q) for q a prime power the Suzuki groups Sz(22n+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. TI-groups The C-groups include as special cases the TI-groups (trivial intersection groups), that are groups in which any two Sylow 2-subgroups have trivial intersection. These were classified by , and the simple ones are of the form PSL2(q), PU3(q), Sz(q) for q a power of 2. References Finite groups