
C-group

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 
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.