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Class two p groups as fixed point free automorphism groups

Citation

Berger, Thomas Robert (1967) Class two p groups as fixed point free automorphism groups. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:11022015-081046019

Abstract

Suppose that AG is a solvable group with normal subgroup G where (|A|, |G|) = 1. Assume that A is a class two odd p group all of whose irreducible representations are isomorphic to subgroups of extra special p groups. If pc ≠ rd + 1 for any c = 1, 2 and any prime r where r2d+1 divides |G| and if CG(A) = 1 then the Fitting length of G is bounded by the power of p dividing |A|.

The theorem is proved by applying a fixed point theorem to a reduction of the Fitting series of G. The fixed point theorem is proved by reducing a minimal counter example. IF R is an extra spec r subgroup of G fixed by A1, a subgroup of A, where A1 centralizes D(R), then all irreducible characters of A1R which are nontrivial on Z(R) are computed. All nonlinear characters of a class two p group are computed.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Dade, E. C.
Thesis Committee:
  • Unknown, Unknown
Defense Date:28 April 1967
Funders:
Funding AgencyGrant Number
NSFUNSPECIFIED
Woodrow Wilson FoundationUNSPECIFIED
CaltechUNSPECIFIED
Record Number:CaltechTHESIS:11022015-081046019
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:11022015-081046019
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9262
Collection:CaltechTHESIS
Deposited By: Leslie Granillo
Deposited On:02 Nov 2015 17:48
Last Modified:02 Nov 2015 17:48

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