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Orbits of finite solvable groups on characters

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Abstract

We prove that if a solvable group A acts coprimely on a solvable group G, then A has a “large” orbit in its corresponding action on the set of ordinary complex irreducible characters of G. This extends (at the cost of a weaker bound) a 2005 result of A. Moretó who obtained such a bound in case that A is a p-group.

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Authors and Affiliations

  1. Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX, 78666, USA

    Thomas Michael Keller & Yong Yang

Authors
  1. Thomas Michael Keller
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  2. Yong Yang
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Correspondence to Thomas Michael Keller.

Additional information

Part of this work was done while the first author was on sabbatical leave and was visiting the University of Wisconsin-Parkside. He thanks the Mathematics Department there for its hospitality.

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Keller, T.M., Yang, Y. Orbits of finite solvable groups on characters. Isr. J. Math. 199, 933–940 (2014). https://doi.org/10.1007/s11856-013-0073-0

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  • DOI: https://doi.org/10.1007/s11856-013-0073-0

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