A characterization of finite soluble groups

Journal article

Let G be a finite soluble group of order m and let ω(xi, ⋯, xn) be a group word. Then the probability that ω(g1, ⋯, gn) = 1 (where (g1, mellip;, gn) is a random n-tuple in G)isatleast 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 Abért has shown that the corresponding probability can take arbitrarily small positive values as n → ∞. © 2007 London Mathematical Society.

Authors: Nikolov, N; Segal, D

• Publication status: Published
• Journal: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
• Volume: 39
• Issue: 2
• Pages: 209-213
• Publication date: 2007-04-01
• DOI: 10.1112/blms/bdl028
• EISSN: 1469-2120
• ISSN: 0024-6093
• Language: English