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Bounding the number of conjugacy classes of a permutation group
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Attila Maróti
Published/Copyright:
July 27, 2005
Abstract
For a finite group G, let k(G) denote the number of conjugacy classes of G. If G is a finite permutation group of degree n > 2, then k(G) ≤ 3(n−1)/2. This is an extension of a theorem of Kovács and Robinson and in turn of Riese and Schmid. If N is a normal subgroup of a completely reducible subgroup of GL(n, q), then k(N ) ≤ q5n. Similarly, if N is a normal subgroup of a primitive subgroup of Sn, then k (N ) ≤ p (n) where p (n) is the number of partitions of n. These bounds improve results of Liebeck and Pyber.
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Published Online: 2005-07-27
Published in Print: 2005-05-25
© de Gruyter
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Articles in the same Issue
- On two conditions on characters and conjugacy classes in finite soluble groups
- Bounding the number of conjugacy classes of a permutation group
- Real conjugacy classes in algebraic groups and finite groups of Lie type
- The number of generators of finite p-groups
- Solvable groups with a given solvable length, and minimal composition length
- Actions of relative Weyl groups II
- Growth rates of amenable groups
Articles in the same Issue
- On two conditions on characters and conjugacy classes in finite soluble groups
- Bounding the number of conjugacy classes of a permutation group
- Real conjugacy classes in algebraic groups and finite groups of Lie type
- The number of generators of finite p-groups
- Solvable groups with a given solvable length, and minimal composition length
- Actions of relative Weyl groups II
- Growth rates of amenable groups
