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Title:  On PRadical PBlocks of Group Algebras 
Author(s):  Laradji, Abdellatif 
Doctoral Committee Chair(s):  Suzuki, Michio 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics 
Abstract:  pRadical pblocks of finite group algebras are studied. Much of the pradical group theory is generalized to pblocks 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 pradical groups is a result of T. Okuyama, who showed that such groups are psolvable. It turns out that the same conclusion could be reached assuming much less. In fact, it is shown that finite groups, whose principal pblocks are pradical, are psolvable. This is not in general true for nonprincipal blocks as illustrated by some examples. Nevertheless, in any case, simple modules in pradical blocks behave somewhat like those in blocks of psolvable groups. A pblock, in which every (modular) simple module has vertices contained in the kernel, is characterized. Such a block enjoys a property much stronger than pradicality. 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 plength 1 psolvable groups, in terms of the ordinary irreducible characters of the principal pblocks, are given. 
Issue Date:  1993 
Type:  Text 
Description:  77 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 1993. 
URI:  http://hdl.handle.net/2142/72540 
Other Identifier(s):  (UMI)AAI9329091 
Date Available in IDEALS:  20141217 
Date Deposited:  1993 
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Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois