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On recognition of alternating groups by prime graph. / Staroletov, Alexey Mikhailovich.
в: Сибирские электронные математические известия, Том 14, 01.01.2017, стр. 994-1010.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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 -
ID: 20337240