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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

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


Authors: S. Evdokimov, M. Muzychuk and I. Ponomarenko
Original publication: Algebra i Analiz, tom 29 (2017), nomer 4.
Journal: St. Petersburg Math. J. 29 (2018), 575-580
MSC (2010): Primary 20B05
DOI: https://doi.org/10.1090/spmj/1507
Published electronically: June 1, 2018
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Abstract | References | Similar Articles | Additional Information

Abstract: Given a prime $ p$, a permutation group is constructed that contains at least $ p^{p-2}$ nonconjugated regular elementary Abelian subgroups of order $ p^3$. This gives the first example of a permutation group with exponentially many nonconjugated regular subgroups.


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Additional Information

S. Evdokimov
Affiliation: Netanya Academic College, Netanya, Israel

M. Muzychuk
Affiliation: Netanya Academic College, Netanya, Israel
Email: muzy@netanya.ac.il

I. Ponomarenko
Affiliation: St. Petersburg Branch, Steklov Institute of Mathematics, Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
Email: inp@pdmi.ras.ru

DOI: https://doi.org/10.1090/spmj/1507
Keywords: Permutation group, regular subgroup, polynomial over finite field
Received by editor(s): February 6, 2017
Published electronically: June 1, 2018
Additional Notes: The first author, S. Evdokimov, is deceased.
Article copyright: © Copyright 2018 American Mathematical Society

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