Question: Question E only. D Let G be a finite group, H a subgroup and g E G. Prove that g-Hg = {g xg : x

Question E only.

D Let G be a finite group, H a subgroup and g E G. Prove that g-Hg = {g xg : x ( H} is a subgroup of G. Prove that |9 Hg) = |H). If G is abelian, what is g Hg equal to? E A subgroup H of G is called normal if g Hg = H for all g E G (see D). Let G = S3 and H1 = {e, (12) }, H2 = fe, (123), (132) }. Hi and H2 are subgroups of G. For each of H1, H2 either prove it is normal or that is not normal

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