A family of permutation groups with exponentially many nonconjugated regular elementary Abelian subgroups

S. Evdokimov; M. Muzychuk; I. Ponomarenko

doi:10.1090/spmj/1507

A family of permutation groups with exponentially many nonconjugated regular elementary Abelian subgroups

S. Evdokimov, M. Muzychuk, I. Ponomarenko

Research output: Contribution to journal › Article › peer-review

Abstract

Given a prime p, a permutation group is constructed that contains at least p^p-2 nonconjugated regular elementary Abelian subgroups of order p³. This gives the first example of a permutation group with exponentially many nonconjugated regular subgroups.

Original language	American English
Pages (from-to)	575-580
Number of pages	6
Journal	St. Petersburg Mathematical Journal
Volume	29
Issue number	4
DOIs	https://doi.org/10.1090/spmj/1507
State	Published - 1 Jan 2018
Externally published	Yes

Keywords

Permutation group
Polynomial over finite field
Regular subgroup

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1090/spmj/1507

Cite this

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title = "A family of permutation groups with exponentially many nonconjugated regular elementary Abelian subgroups",

abstract = "Given a prime p, a permutation group is constructed that contains at least pp-2 nonconjugated regular elementary Abelian subgroups of order p3. This gives the first example of a permutation group with exponentially many nonconjugated regular subgroups.",

keywords = "Permutation group, Polynomial over finite field, Regular subgroup",

author = "S. Evdokimov and M. Muzychuk and I. Ponomarenko",

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AU - Muzychuk, M.

AU - Ponomarenko, I.

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N2 - Given a prime p, a permutation group is constructed that contains at least pp-2 nonconjugated regular elementary Abelian subgroups of order p3. This gives the first example of a permutation group with exponentially many nonconjugated regular subgroups.

AB - Given a prime p, a permutation group is constructed that contains at least pp-2 nonconjugated regular elementary Abelian subgroups of order p3. This gives the first example of a permutation group with exponentially many nonconjugated regular subgroups.

KW - Permutation group

KW - Polynomial over finite field

KW - Regular subgroup

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U2 - 10.1090/spmj/1507

DO - 10.1090/spmj/1507

M3 - Article

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JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

IS - 4

ER -

A family of permutation groups with exponentially many nonconjugated regular elementary Abelian subgroups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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