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Character Theory and Length Problems

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Finite and Locally Finite Groups

Part of the book series: NATO ASI Series ((ASIC,volume 471))

Abstract

We discuss some length questions in the theory of finite solvable groups for which character theory has proven useful. We discuss some open problems, some techniques of proof for various character and module theoretic results arising in this context, as well as the applications of these results to the length problems themselves. As this is an expository paper, most of our results appeared elsewhere. An exception is a linear bound on the Fitting height of groups accepting a fixed point free abelian group of automorphisms of square-free odd exponent, which, although it follows easily from known results, does not seem to have been noticed before.

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Authors and Affiliations

  1. Department of Mathematics, University of Florida, Gainesville, Florida, 32611, USA

    A. Turull

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  1. A. Turull
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Editors and Affiliations

  1. Department of Mathematics, University of Manchester, Manchester, UK

    B. Hartley

  2. Department of Mathematics, University of Oregon, Eugene, Oregon, USA

    G. M. Seitz

  3. UMIST, Manchester, UK

    A. V. Borovik  & R. M. Bryant  & 

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Turull, A. (1995). Character Theory and Length Problems. In: Hartley, B., Seitz, G.M., Borovik, A.V., Bryant, R.M. (eds) Finite and Locally Finite Groups. NATO ASI Series, vol 471. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0329-9_14

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  • DOI: https://doi.org/10.1007/978-94-011-0329-9_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4145-4

  • Online ISBN: 978-94-011-0329-9

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