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Problems with normal subgroups

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Problems with normal subgroups

1. Let N₁, ..., N_k be normal subgroups of a finite group G. If G = N₁N₂ ...N_k (the set of all elements of the form a₁a2...a_k with a j in N _j) and |G| = |N₁| . |N₂| . |N₃| ... |N_k|, prove that G = N₁ x N₂ x N₃x ... x N_k.

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Algebra: Problems with normal subgroups

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Algebra: Problems with normal subgroups

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