On the prime graph question for almost simple groups with an alternating socle

被引：6

作者：

Bachle, Andreas ^{[1
]}

Caicedo, Mauricio ^{[1
]}

机构：

[1] Vrije Univ Brussel, Dept Math, Pl Laan 2, B-1050 Brussels, Belgium

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2017年 / 27卷 / 03期

关键词：

Group rings; finite groups; prime graph question; symmetric groups; alternating groups; INTEGRAL GROUP-RINGS; ZASSENHAUS CONJECTURE; TORSION UNITS;

D O I：

10.1142/S0218196717500175

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be an almost simple group with socle A(n), the alternating group of degree n. We prove that there is a unit of order pq in the integral group ring of G if and only if there is an element of that order in G provided p and q are primes greater than n/3. We combine this with some explicit computations to verify the prime graph question for all almost simple groups with socle A(n) if n <= 17.

引用

页码：333 / 347

页数：15

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