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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 31 Jan 2024 18:50:23 +0000Class two p groups as fixed point free automorphism groups
https://resolver.caltech.edu/CaltechTHESIS:11022015-081046019
Authors: {'items': [{'id': 'Berger-T-R', 'name': {'family': 'Berger', 'given': 'Thomas Robert'}}]}
Year: 1967
DOI: 10.7907/NYAT-FG53
<p>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 p<sup>c</sup> ≠ r<sup>d</sup> + 1 for any c = 1, 2 and any prime r where r<sup>2d+1</sup> divides |G| and if C<sub>G</sub>(A) = 1 then the Fitting length of G is bounded by the power of p dividing |A|.</p>
<p>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 A<sub>1</sub>, a subgroup of A, where A<sub>1</sub> centralizes D(R), then all irreducible characters of A<sub>1</sub>R which are nontrivial on Z(R) are computed. All nonlinear characters of a class two p group are computed. </p>
https://thesis.library.caltech.edu/id/eprint/9262