Factoring Subgroups and Factor Groups of the Unit Group Modulo n

Joseph A. Gallian; Shahriyar Roshan Zamir

doi:10.1080/0025570X.2022.2094167

Factoring Subgroups and Factor Groups of the Unit Group Modulo n

Joseph A. Gallian, Shahriyar Roshan Zamir

Mathematics & Statistics

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

Abstract

Summary: We introduce several ways of producing subgroups of U(n), the group of units of Z_n. Our results find the structure of these various subgroups in terms of external direct product of cyclic groups. We then use our classifications to give descriptions of elements of U(n) that form a subgroup of U(n) with a desired cyclic group decomposition. This includes a description of elements that form a Sylow p-subgroup.

Original language	English (US)
Pages (from-to)	376-388
Number of pages	13
Journal	Mathematics Magazine
Volume	95
Issue number	4
DOIs	https://doi.org/10.1080/0025570X.2022.2094167
State	Published - 2022

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© 2022 Joseph A. Gallian and Shahriyar Roshan Zamir 2022. All Rights Reserved.

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abstract = "Summary: We introduce several ways of producing subgroups of U(n), the group of units of Zn. Our results find the structure of these various subgroups in terms of external direct product of cyclic groups. We then use our classifications to give descriptions of elements of U(n) that form a subgroup of U(n) with a desired cyclic group decomposition. This includes a description of elements that form a Sylow p-subgroup.",

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Factoring Subgroups and Factor Groups of the Unit Group Modulo n

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