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Some class size conditions implying solvability of finite groups
-
Antonio Beltrán
and
María José Felipe
Published/Copyright:
February 12, 2007
Abstract
Let G be a finite group. We show that when the conjugacy class sizes of G are {1, m, n, mn}, with m and n positive integers such that (m, n) = 1, then G is solvable. As a consequence, we obtain that G is nilpotent and that m = pa and n = qb for two primes p and q.
Received: 2005-11-03
Published Online: 2007-02-12
Published in Print: 2006-11-28
© Walter de Gruyter
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Articles in the same Issue
- Crossover Morita equivalences for blocks of the covering groups of the symmetric and alternating groups
- On a theorem of Artin. II
- Cycle index methods for finite groups of orthogonal type in odd characteristic
- Characterization of injectors in finite soluble groups
- Some class size conditions implying solvability of finite groups
- On t-pure and almost pure exact sequences of LCA groups
- Translation equivalent elements in free groups
- On representing words in the automorphism group of the random graph
