The proportion of fixed-point-free elements of a transitive permutation group

DOI10.1080/00927879308824728zbMath0783.20002OpenAlexW2115090518MaRDI QIDQ3135712

Paul J. Gies, Judy Leavitt, Walter Dabrowski, David T. Ose, Nigel Boston, David A. Jackson, Tuval Foguel

Publication date: 10 October 1993

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1187&context=mathfacpub

zbMATH Keywords

generating functionswreath productsnilpotent groupstransitive permutation groupfixed-point-free elementssharply 2- transitive

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Primitive groups (20B15) General theory for finite permutation groups (20B05) Multiply transitive finite groups (20B20)

Related Items (17)

An Erdős-Ko-Rado theorem for finite 2-transitive groups ⋮ Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements ⋮ Primitive permutation groups and derangements of prime power order. ⋮ Conjugacy class properties of the extension of \(\text{GL}(n,q)\) generated by the inverse transpose involution. ⋮ Conjugacy classes of derangements in finite transitive groups ⋮ Braided Line and Counting Fixed Points ofGL(d, 𝔽_q) ⋮ Bounds for fixed point free elements in a transitive group and applications to curves over finite fields ⋮ Derangements in subspace actions of finite classical groups ⋮ Derangements in wreath products of permutation groups ⋮ Fixed point polynomials of permutation groups. ⋮ Derangements in finite classical groups for actions related to extension field and imprimitive subgroups and the solution of the Boston–Shalev conjecture ⋮ On a relation between the rank and the proportion of derangements in finite transitive permutation groups. ⋮ On a theorem of Jordan ⋮ On the number of derangements and derangements of prime power order of the affine general linear groups ⋮ Permutation codes ⋮ On cyclic semi-regular subgroups of certain 2-transitive permutation groups ⋮ On fixed points of permutations.

Uses Software

• Cayley

Cites Work

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• On the degrees of primitive permutation groups
• Primitive Permutation Groups Containing an Element of Large Prime Order
• Finite Permutation Groups and Finite Simple Groups
• The probability of generating a classical group

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