M. R. Darafsheh
Abstract
We will find the structure of finite groups G = AB where A and B are subgroups of G with A ≅ A r , the alternating group on r letters, and B ≅ S n , the symmetric group on n letters, where r, n ≥ 5.
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We will find the structure of finite groups G = AB where A and B are subgroups of G with A ≅ A r , the alternating group on r letters, and B ≅ S n , the symmetric group on n letters, where r, n ≥ 5.
Key concepts: Alternating group, Mathematics, Group (periodic table), Covering groups of the alternating and symmetric groups, Symmetric group, Finite group, Combinatorics, Product (mathematics)