Relatively Maximal Subgroups of Odd Index in Symmetric Groups
Let X be a class of finite groups which contains a group of order 2 and is closed under subgroups, homomorphic images, and extensions. We define the concept of an X-admissible diagram representing a natural number n. Associated with each n are finitely many such diagrams, and they all can be found e...
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| Veröffentlicht in: | Algebra and logic 2022-05, Vol.61 (2), p.104-124 |
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| container_title | Algebra and logic |
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| creator | Vasil’ev, A. S. Revin, D. O. |
| description | Let X be a class of finite groups which contains a group of order 2 and is closed under subgroups, homomorphic images, and extensions. We define the concept of an X-admissible diagram representing a natural number n. Associated with each n are finitely many such diagrams, and they all can be found easily. Admissible diagrams representing a number n are used to uniquely parametrize conjugacy classes of maximal X-subgroups of odd index in the symmetric group Sym
n
, and we define the structure of such groups. As a consequence, we obtain a complete classification of submaximal X-subgroups of odd index in alternating groups. |
| doi_str_mv | 10.1007/s10469-022-09680-0 |
| format | Article |
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n
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| subjects | Algebra Group theory Mathematical Logic and Foundations Mathematical research Mathematics Mathematics and Statistics Subgroups Symmetric functions |
| title | Relatively Maximal Subgroups of Odd Index in Symmetric Groups |
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