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  3. suppose that a group g acts on its power set p(g)

Suppose that a group G acts on its power set P(G) by conjugation. a) If H?G, prove...

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Advance Math

Suppose that a group G acts on its power set P(G) byconjugation.

a) If H?G, prove that the normalizer of N(H) is the largestsubgroup K of G such that HEK. In particular, if G is finite showthat |H| divides |N(H)|.

b) Show that H?G??every element B?OH is a subgroup of G withB?=H.

c) Prove that HEG??|OH|= 1.

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