Let G be a group and a an element of G. the centralizer of a is the set C(a)={g in G: ga=ag}. prove that C(a) is a subgroup of G.
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Originally Posted by nikie1o2 Let G be a group and a an element of G. the centralizer of a is the set C(a)={g in G: ga=ag}. prove that C(a) is a subgroup of G. What've you tried? Prove that the group's unit is contained in and also that Tonio
Originally Posted by nikie1o2 Let G be a group and a an element of G. the centralizer of a is the set C(a)={g in G: ga=ag}. prove that C(a) is a subgroup of G. Let . Then and . So , and . Now observe that . So , that is, . Since clearly , then it follows that is a subgroup of
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