University of Illinois Urbana-Champaign

On P-Radical P-Blocks of Group Algebras

Laradji, Abdellatif

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Description

Title
On P-Radical P-Blocks of Group Algebras
Author(s)
Laradji, Abdellatif
Issue Date
1993
Doctoral Committee Chair(s)
Suzuki, Michio
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Abstract
  • p-Radical p-blocks of finite group algebras are studied. Much of the p-radical group theory is generalized to p-blocks through R. Knorr's work on simple induction and restriction pairs. In addition, several results concerning such blocks are proved.
  • The most interesting fact known about p-radical groups is a result of T. Okuyama, who showed that such groups are p-solvable. It turns out that the same conclusion could be reached assuming much less. In fact, it is shown that finite groups, whose principal p-blocks are p-radical, are p-solvable. This is not in general true for non-principal blocks as illustrated by some examples. Nevertheless, in any case, simple modules in p-radical blocks behave somewhat like those in blocks of p-solvable groups.
  • A p-block, in which every (modular) simple module has vertices contained in the kernel, is characterized. Such a block enjoys a property much stronger than p-radicality. If, in addition, every simple module in this block has vertices conjugate to a defect group of the block, further characterizations are derived. As a consequence, some characterizations of p-length 1 p-solvable groups, in terms of the ordinary irreducible characters of the principal p-blocks, are given.
Graduation Semester
1993
Type of Resource
text
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http://hdl.handle.net/2142/72540

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