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Examples of 3-dimensional 1-cohomology for absolutely irreducible modules of finite simple groups
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Published/Copyright:
September 19, 2008
Abstract
It is known that for finite simple groups it is possible for a faithful absolutely irreducible module to have 1-cohomology of dimension at least 3. However, until now no explicit examples have been found. We present two explicit examples where the dimension is exactly 3. It remains an open question as to whether the dimension can be bigger than 3.
Received: 2007-07-06
Revised: 2007-10-15
Published Online: 2008-09-19
Published in Print: 2008-September
© de Gruyter 2008
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Articles in the same Issue
- Generation gaps and abelianized defects of free products
- Abelian-by-polycyclic groups of homological type FP3
- Conjugacy in lattice-ordered groups and right ordered groups
- An approach to duality on abelian precompact groups
- Special abelian Moufang sets of finite Morley rank
- Cross characteristic representations of 3D4(q) are reducible over proper subgroups
- Examples of 3-dimensional 1-cohomology for absolutely irreducible modules of finite simple groups
- Short two-variable identities for finite groups
- Schur indices and commutators in supersolvable groups
- Two dual questions on zeros of characters of finite groups
- Supercharacters of the adjoint group of a finite radical ring
