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The Exponent of a Group: Properties, Computations and Applications

In: Discrete Mathematics and Applications

Author

Listed:
  • Dorin Andrica

    (“Babeş-Bolyai” University)

  • Sorin Rădulescu

    (Institute of Mathematical Statistics and Applied Mathematics)

  • George Cătălin Ţurcaş

    (“Babeş-Bolyai” University
    The Institute of Mathematics of the Romanian Academy “Simion Stoilow”)

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.

Suggested Citation

  • Dorin Andrica & Sorin Rădulescu & George Cătălin Ţurcaş, 2020. "The Exponent of a Group: Properties, Computations and Applications," Springer Optimization and Its Applications, in: Andrei M. Raigorodskii & Michael Th. Rassias (ed.), Discrete Mathematics and Applications, pages 57-108, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-55857-4_4
    DOI: 10.1007/978-3-030-55857-4_4
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