Abstract algebra in the Encyclopedia. proof Prove that a group homomorphism maps the identity to the identity and inverses to inverses. proof Prove that the kernel of a homomorphism from a group is a subgroup of that group. then the following are equivalent: proof Prove that a group of order 56 has a normal Sylow p-subgroup for some prime dividing its order. proof Prove that a group of order 312 has a normal Sylow p-subgroup. However, as a favor, I ask that you make clear which material is yours and which is from the main version of the text.

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