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.
