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RESEARCH PRODUCT

Transitive permutation groups in which all derangements are involutions

Thomas Michael KellerMark L. LewisI. M. IsaacsAlexander Moretó

subject

CombinatoricsSubgroupAlgebra and Number TheorySymmetric groupPrimitive permutation groupElementary abelian groupAbelian groupFrobenius groupCyclic permutationMathematicsNon-abelian group

description

AbstractLet 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.

yearjournalcountryeditionlanguage
2006-11-01Journal of Pure and Applied Algebra
10.1016/j.jpaa.2005.11.005http://dx.doi.org/10.1016/j.jpaa.2005.11.005