Let H be a subgroup of G such that x^2 lies in H for x in G then H is a normal subgroup of G

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If H be a subgroup of G, such that x^2€H all x€G, Prove that H is Normal in G|Group Theory If H be a subgroup of G, such that x^2€H all x€G, Prove that H is Normal in G|Group Theory
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If x^2 = e for all x in G then G is an abelian group proof If x^2 = e for all x in G then G is an abelian group proof
A subgroup H of a group G is a normal subgroup of G if and only if ghg^-1 ∈ H ∀ g∈G and h∈H. A subgroup H of a group G is a normal subgroup of G if and only if ghg^-1 ∈ H ∀ g∈G and h∈H.
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Problem 1. Let G be a group. Show that if H is a subgroup of G of index 2, then H is a normal subgr… Problem 1. Let G be a group. Show that if H is a subgroup of G of index 2, then H is a normal subgr…
Let H be subgroup of a group G and let a, b∈G.Then i) aH =bH iff a^-1b∈ H ii)Ha=Hb iff ab^-1∈H Let H be subgroup of a group G and let a, b∈G.Then i) aH =bH iff a^-1b∈ H ii)Ha=Hb iff ab^-1∈H
H is a subgroup of index 2 in G then H is a normal subgroup of G H is a subgroup of index 2 in G then H is a normal subgroup of G