Resumen de Groups With the Same Prime Graph as a CIT Simple Group

Behrooz Khosravi, Behman Khosravi, Bahman Khosravi

• Let G be a finite group. The prime graph of G is the graph whose vertex set is the set of all prime divisors of |G|, and two distinct primes p and q are joined by an edge if and only if G contains an element of order pq. A group M is called a CIT group or a C22 group if M is of even order and the centralizer of any involution is a 2-group. In this paper we determine finite groups G such that their prime graph is the same prime graph of M, where M is a CIT simple group. As a consequence of this result, we prove that if p>7 is a Mersenne prime or a Fermat prime, then PSL(2,p) is uniquely determined by its prime graph. Also we prove a few results by using the main theorem.