Question

In: Advanced Math

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

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

a) If H≤G, prove that the normalizer of N(H) is the largest subgroup K of G such that HEK. In particular, if G is finite show that |H| divides |N(H)|.

b) Show that H≤G⇐⇒every element B∈OH is a subgroup of G with B∼=H.

c) Prove that HEG⇐⇒|OH|= 1.

Solutions

Expert Solution

Colby Messinger answered 2 years ago
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