Recall that the center of a group G is the set Z(G)={x∈G:xg=gx for all g∈G}.
a. Calcula...
Mathematics, 16.04.2020 00:22, chris858232
Recall that the center of a group G is the set Z(G)={x∈G:xg=gx for all g∈G}.
a. Calculate the center of S3.
b. Calculate the center of GL2(R).
c. Show that the center of any group G is a normal subgroup of G .
d. If G/Z(G) is cyclic, show that G is abelian.
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