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Totally imprimitive permutation groups with the cyclic-block property
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A. O. Asar
Published/Copyright:
August 13, 2010
Abstract
Totally imprimitive p-groups satisfying the cyclic-block property are investigated. It is shown that in these groups any two blocks either are disjoint or one is contained in the other, and so the set of all blocks of the same size forms just one block system. Furthermore the non-FC-subgroups of these groups are transitive. For each prime p totally imprimitive p-subgroups of FSym(ℕ*) satisfying the cyclic-block property are constructed, which are not minimal non-FC-groups.
Received: 2009-09-16
Revised: 2010-03-30
Published Online: 2010-08-13
Published in Print: 2011-January
© de Gruyter 2011
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Articles in the same Issue
- Conway's group and octonions
- Strongly real elements of orthogonal groups in even characteristic
- A rigid triple of conjugacy classes in G2
- On the shortest identity in finite simple groups of Lie type
- Solomon's induction in quasi-elementary groups
- Character degree sums in finite nonsolvable groups
- Decomposing tensor products and exterior and symmetric squares
- On representations of groups of odd order
- An existence criterion for Hall subgroups of finite groups
- Covering certain wreath products with proper subgroups
- Totally imprimitive permutation groups with the cyclic-block property
- On representations of Artin–Tits and surface braid groups
- On Property (FA) for wreath products
