Factoring Subgroups and Factor Groups of the Unit Group Modulo n

Joseph A. Gallian, Shahriyar Roshan Zamir

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)376-388
Number of pages13
JournalMathematics Magazine
Issue number4
StatePublished - 2022
Externally publishedYes

Bibliographical note

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


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