Factorizations of the sporadic simple groups
Copyright policy )Factorizations of the sporadic simple groups
Let G be one of the 26 (presently known) sporadic finite simple groups. We assume that all simple subgroups of G are known groups, and prove the following result. Theorem. Let \(G=AB\) where A, B are proper non-Abelian simple subgroups of G. Then one of the following holds: (1) \(G=M_{12}\), \(A\cong A_ 5\), \(L_ 2(11)\), or \(M_{11}\), \(B\cong M_{11};\) (2) \(G=M_{24}\), \(A\cong L_ 2(23)\), \(B\cong M_{22}\) or \(M_{23}\) or \(A\cong L_ 2(7)\), \(B\cong M_{23};\) (3) \(G=Suz\), \(A\cong U_ 5(2)\), \(B\cong G_ 2(4);\) (4) \(G=Co_ 1\), \(A\cong G_ 2(4)\), \(B\cong Co_ 2;\) The factorizations (1)-(4) exist.
simple subgroups, Products of subgroups of abstract finite groups, sporadic finite simple groups, factorizations, Simple groups: sporadic groups
simple subgroups, Products of subgroups of abstract finite groups, sporadic finite simple groups, factorizations, Simple groups: sporadic groups
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