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Subgroups of direct products of groups invariant under the action of permutations on factors

, 2020
We study subgroups of the direct product of two groups invariant under the action of permutations on factors. An invariance criterion for the subdirect product of two groups under the action of permutations on factors is put forward.
D. A. Burov
semanticscholar   +1 more source

Union of products of subgroups in finite groups

Communications in Algebra
Let G be a group and A, B, C be subgroups of G. In this paper, we prove that if G=AB∪BC, then G = AB or G = BC. But, in general, G=AB∪AC does not imply that G = AB or G = AC.
Hangyang Meng   +2 more
semanticscholar   +1 more source

On some products of groups

Proceedings of the Edinburgh Mathematical Society
A classical result of Reinhold Baer states that a group G = XN, which is the product of two normal supersoluble subgroups X and N, is supersoluble if and only if Gʹ is nilpotent.
Luigi Iorio, M. Trombetti
semanticscholar   +1 more source

𝜏-Tilting finiteness of group algebras of semidirect products of abelian 𝑝-groups and abelian 𝑝′-groups

Journal of group theroy
Demonet, Iyama and Jasso introduced a new class of finite-dimensional algebras, 𝜏-tilting finite algebras. It was shown by Eisele, Janssens and Raedschelders that tame blocks of group algebras of finite groups are always 𝜏-tilting finite.
Naoya Hiramae, Yuta Kozakai
semanticscholar   +1 more source

On exact products of two dihedral groups

Communications in Algebra
An exact product of two finite groups H and K is a finite group X which contains H and K as subgroups, satisfying X=HK and H∩K={1X}. In this paper, we provide a classification of the exact products of two dihedral groups of orders 2m and 2n for all odd ...
Kan Hu, Hao Yu
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On exact products of a cyclic group and a dihedral group

Communications in Algebra
A finite group G is an exact product of two subgroups A and B if G = AB and A∩B={1G}. In this paper, for all odd numbers k≥3, using the theory of skew morphisms and associated extended power functions, we present a classification of exact products of a ...
Kan Hu, István Kovács, Young Soo Kwon
semanticscholar   +1 more source

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