The Exponent of a Group: Properties, Computations and Applications

Dorin Andrica (), Sorin Rădulescu () and George Cătălin Ţurcaş ()
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Dorin Andrica: “Babeş-Bolyai” University
Sorin Rădulescu: Institute of Mathematical Statistics and Applied Mathematics
George Cătălin Ţurcaş: “Babeş-Bolyai” University

A chapter in Discrete Mathematics and Applications, 2020, pp 57-108 from Springer

Abstract: Abstract This material is a systematic presentation of the exponent of a group with properties, examples, and explicit computations. Some of the results and connexions we present are original or they are presented in a new form. The last section explores general results about the exponent of certain finite groups of matrices. We will explicitly compute the exponent for SL 2 ( ℤ ∕ p n ℤ ) $$ \operatorname {\mathrm {SL}}_2(\mathbb Z/p^n \mathbb Z)$$ and GL 2 ( ℤ ∕ p n ℤ ) $$ \operatorname {\mathrm {GL}}_2(\mathbb Z/p^n \mathbb Z)$$ , when p ∈{2, 3} and n is a positive integer.

Keywords: Exponent of a group; fe-Group; Symmetric group; Alternating group; Dihedral group; Automorphism group; Direct product; Prüfer p-group; Landau function g(n); Group action; Burnside lemma; Frobenius theorem; Heisenberg matrix group; Kummer’s theorem; 20Axx; 20B05; 20B30; 20D20; 20D45; 20E36 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-55857-4_4

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DOI: 10.1007/978-3-030-55857-4_4

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