Аннотация
The prime graph Γ(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 A n (S n ) denote the alternating (symmetric) group of degree n. We prove that if G is a finite group with Γ(G)=Γ(A n ) or Γ(G)=Γ(S n ), where n≥19, then there exists a normal subgroup K of G and an integer t such that A t ≤G(K)≤S t and |K| is divisible by at most one prime greater than n/2.
Язык оригинала | английский |
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Страницы (с-по) | 3905-3914 |
Число страниц | 10 |
Журнал | Communications in Algebra |
Том | 47 |
Номер выпуска | 9 |
DOI | |
Состояние | Опубликовано - 2 сен 2019 |