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moont14263
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If G is a finite group and M is a maximal subgroup, H is a subgroup of G not contained in M. Then G=HM.
Is this true?
Is this true?
A maximal subgroup of a group is a subgroup that cannot be properly contained in any larger subgroup.
A maximal subgroup is not necessarily a normal subgroup, meaning it may not be invariant under conjugation by elements of the larger group.
Yes, a group can have multiple maximal subgroups, but they will all be distinct from each other.
A subgroup can be determined to be maximal by checking if it is not contained in any larger subgroup of the group.
No, there could be multiple different maximal subgroups for a given group, depending on the structure and properties of the group.