efine xHx-1= {xhxh Hx is a subgroup of G. His cyclic, then xHx E H is cyc
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Transcribed Image Text:1. Let G be a group and let H be a subgroup of G. For any fixed x in
G, define xHx1 = {xhx-¹|hEH). Prove the following.
a. xHx¹ is a subgroup of G.
b. If His cyclic, then xHx-¹ is cyclic.
c. If His Abelian, then xHx-¹ is Abelian.
The group xHx¹ is called a conjugate of H. (Note that conjuga-
tion preserves structure.)
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