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A characterization of finite soluble groups

Abstract:
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.
Publication status:
Published

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Publisher copy:
10.1112/blms/bdl028

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY More from this journal
Volume:
39
Issue:
2
Pages:
209-213
Publication date:
2007-04-01
DOI:
EISSN:
1469-2120
ISSN:
0024-6093
Language:
English
Pubs id:
pubs:2544
UUID:
uuid:09f30888-19f4-4f16-b7aa-bba375c8187f
Local pid:
pubs:2544
Source identifiers:
2544
Deposit date:
2012-12-19

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