The orders of subgroup products and coset products

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, JAPAN

Abstract

A sect is a subset of a group given by the product of a finite number of subgroups. It is generally not a direct product nor even a subgroup of the group. For finite groups, the orders of sects are their basic invariants. In this paper we describe properties of the orders of sects, such as divisibility and inequalities, which give constraints on the possible values of the orders of sects. We further consider clans, which are subsets of groups given by products of finite numbers of cosets. We also describe properties of their orders.

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References

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Transactions on Combinatorics
Volume 14, Issue 4 - Serial Number 4
December 2025
Pages 223-250

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History

  • Receive Date: 21 May 2024
  • Revise Date: 05 August 2024
  • Accept Date: 19 August 2024
  • Published Online: 01 December 2025

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