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osu1124221435.pdf (372.33 KB)
ETD Abstract Container
Abstract Header
On the sources of simple modules in nilpotent blocks
Author Info
Salminen, Adam D.
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1124221435
Abstract Details
Year and Degree
2005, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
Let G be a finite group and let k be an algebraically closed field of characteristic p. If b is a nilpotent block of kG with defect group P, then there is a unique isomorphism class of simple kGb-modules and Puig proved that the source of this module is an endo-permutation kP-module. It is conjectured that the image of this source is always torsion in the Dade group. Let H be a finite group and let P be a p-subgroup of Aut(H). Also let c be a defect zero block of kH. If c is a P-stable and BrP (c) = 0, then c is a nilpotent block of k(H P) and k(H P)c has P as a defect group. In this dissertation, we will investigate the sources of the simple k(H P)c-modules when P = Cp × Cp. Suppose that we can find an H and c as above such that a source of a simple k(HP)c-module is not torsion in the Dade group. Then we can find H and c as above with H a central p-extension of a simple group. When p "e 3 we can also show that H can be found in a quite restrictive subset of simple groups.
Committee
Markus Linckelmann (Advisor)
Pages
96 p.
Subject Headings
Mathematics
Keywords
block theory
;
Puig's conjecture
;
Source algebra
;
Nilpotent blocks
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Citations
Salminen, A. D. (2005).
On the sources of simple modules in nilpotent blocks
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1124221435
APA Style (7th edition)
Salminen, Adam.
On the sources of simple modules in nilpotent blocks.
2005. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1124221435.
MLA Style (8th edition)
Salminen, Adam. "On the sources of simple modules in nilpotent blocks." Doctoral dissertation, Ohio State University, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=osu1124221435
Chicago Manual of Style (17th edition)
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Document number:
osu1124221435
Download Count:
913
Copyright Info
© 2005, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.