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Suzuki, Michio Laradji, Abdellatif 2014-12-17T23:17:47Z 2014-12-17T23:17:47Z 10000-01-01 1993 1993 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. Made available in DSpace on 2014-12-17T23:17:47Z (GMT). No. of bitstreams: 1 9329091.pdf: 2515719 bytes, checksum: 59d3bc2a6181018bc344209affc81353 (MD5) Previous issue date: 1993 Embargo set by: Seth Robbins for item 72708 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 77 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1993. http://hdl.handle.net/2142/72540 (UMI)AAI9329091 Mathematics On P-Radical P-Blocks of Group Algebras text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.