Generalizing Exercise 51, let S be any subset of a group G. a. Show that H s

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Generalizing Exercise 51, let S be any subset of a group G.

a. Show that H_s = {x ∈ G| xs = sx for all s ∈ S} is a subgroup of G.

b. In reference to part (a), the subgroup H_G is the center of G. Show that H_Gis an abelian group.

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A First Course In Abstract Algebra

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Authors: John Fraleigh

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Generalizing Exercise 51, let S be any subset of a group G. a. Show that H s

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a Closure Let x y H S Then xs sx and ys sy for all s S We then have xys xys xsy xsy sxy sxy for al...View the full answer

A First Course In Abstract Algebra

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