University of Isfahan Transactions on Combinatorics 2251-8657 14 4 2025 12 01 The orders of subgroup products and coset products 223 250 28670 10.22108/toc.2024.141562.2176 EN Shigeru Takamura Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, JAPAN Journal Article 2024 05 21 A <em>sect </em>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 <em>clans</em>, which are subsets of groups given by products of finite numbers of cosets. We also describe properties of their orders. https://toc.ui.ac.ir/article_28670_ebc3ac219eb683b98452f6d44ee439b0.pdf