The prime graph GK(G) of a finite group G is the graph whose vertex set is the set of prime divisors of |G| and in which two distinct vertices r and s are adjacent if and only if there exists an element of G of order rs. Let Altn denote the alternating group of degree n. Assume that p ≤ 13 is a prime and n is an integer such that p ≥ n ≥ p+3. We prove that if G is a finite group such that GK(G) = GK(Altn), then G has a unique nonabelian composition factor, and this factor is isomorphic to Altt, where p ≥ t ≥ p + 3.
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- 1.01 МАТЕМАТИКА