Search results for "Primitive permutation group"

showing 2 items of 2 documents

Characterizing normal Sylow p-subgroups by character degrees

2012

Abstract Suppose that G is a finite group, let p be a prime and let P ∈ Syl p ( G ) . We prove that P is normal in G if and only if all the irreducible constituents of the permutation character ( 1 P ) G have degree not divisible by p.

Finite groupAlgebra and Number TheoryDegree (graph theory)010102 general mathematicsSylow theoremsPrimitive permutation group01 natural sciencesPrime (order theory)Characters of finite groupsCharacter degrees010101 applied mathematicsCombinatoricsPermutationCharacter (mathematics)0101 mathematicsMathematicsJournal of Algebra
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Transitive permutation groups in which all derangements are involutions

2006

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.

CombinatoricsSubgroupAlgebra and Number TheorySymmetric groupPrimitive permutation groupElementary abelian groupAbelian groupFrobenius groupCyclic permutationMathematicsNon-abelian groupJournal of Pure and Applied Algebra
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