TY - JOUR

T1 - On recognition of alternating groups by prime graph

AU - Staroletov, Alexey Mikhailovich

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - Alternating group

KW - Prime graph

KW - Simple groups

KW - FINITE SIMPLE-GROUPS

KW - alternating group

KW - simple groups

KW - RECOGNIZABILITY

KW - prime graph

UR - http://www.scopus.com/inward/record.url?scp=85063496579&partnerID=8YFLogxK

U2 - 10.17377/semi.2017.14.084

DO - 10.17377/semi.2017.14.084

M3 - Article

AN - SCOPUS:85063496579

VL - 14

SP - 994

EP - 1010

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -