A characterization of finite soluble groups

被引：11

作者：

Nikolov, Nikolay ^{[1
]}

Segal, Dan

机构：

[1] Univ Oxford New Coll, Oxford OX1 3BN, England

[2] Univ Oxford All Souls Coll, Oxford OX1 4AL, England

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2007年 / 39卷

关键词：

D O I：

10.1112/blms/bdl028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite soluble group of order m and let w (x(1),..., x(n)) be a group word. Then the probability that w (g(1),..., g(n)) = 1 (where (g(1),..., g(n)) is a random n-tuple in G) is at least p(-(m-t)), where p is the largest prime divisor of m and t is the number of distinct primes dividing m. This contrasts with the case of a non-soluble group G, for which Abert has shown that the corresponding probability can take arbitrarily small positive values as n -> infinity.

引用

页码：209 / 213

页数：5