What is "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

• the projective special linear groups PSL(p) for p a Fermat or Mersenne prime
• the projective special linear groups PSL(9)
• the projective special linear groups PSL(2) for n≥2
• the projective special linear groups PSL(q) for q a prime power
• the Suzuki groups Sz(2) for n≥1
• the projective unitary groups PU(q) for q a prime power