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|Title:||On P-Radical P-Blocks of Group Algebras|
|Doctoral Committee Chair(s):||Suzuki, Michio|
|Department / Program:||Mathematics|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|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.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1993.
|Date Available in IDEALS:||2014-12-17|