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Transitive permutation groups in which all derangements are involutions |
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| Authors: | IM Isaacs Alexander Moretó |
| Institution: | a Department of Mathematics, University of Wisconsin Madison, WI 53706, USA b Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX 78666-4616, USA c Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA d Departament d’Àlgebra, Universitat de València, 46100 Burjassot. València, Spain |
| Abstract: | Let G be a transitive permutation group in which all derangements are involutions. We prove that G is either an elementary abelian 2-group or is a Frobenius group having an elementary abelian 2-group as kernel. We also consider the analogous problem for abstract groups, and we classify groups G with a proper subgroup H such that every element of G not conjugate to an element of H is an involution. |
| Keywords: | primary 20B10 secondary 20D99 |
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