(a) Verify that if H is a subgroup of G, and a E G, then aHa- 1 is a subgroup of G.(b)
Chapter 58, Problem 58.10(choose chapter or problem)
(a) Verify that if H is a subgroup of G, and a E G, then aHa- 1 is a subgroup of G.(b) Prove that if H is a finite subgroup of G, and a E G, then laHa-11 = IH I. (Suggestion:The mapping h t->- aha-I is one-to-one.)(c) Explain why if H is a Sylow p-subgroup ofa finite group, then so is each conjugate of H.(d) Prove that if a finite group has only one Sylow p-subgroup for some prime p, then thatsubgroup must be normal.
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