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Israel Journal of Mathematics

, Volume 229, Issue 1, pp 181–191 | Cite as

Permutation representations of nonsplit extensions involving alternating groups

  • Robert M. Guralnick
  • Martin W. LiebeckEmail author
Article
  • 29 Downloads

Abstract

L. Babai has shown that a faithful permutation representation of a nonsplit extension of a group by an alternating group Ak must have degree at least \(k^2(\frac{1}{2}-o(1))\), and has asked how sharp this lower bound is. We prove that Babai’s bound is sharp (up to a constant factor), by showing that there are such nonsplit extensions that have faithful permutation representations of degree \(\frac{3}{2}k(k-1)\). We also reprove Babai’s quadratic lower bound with the constant 1/2 improved to 1 (by completely different methods).

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Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Department of MathematicsImperial CollegeLondonUK

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