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.

What is the equation and solution for the sentence? the sum of a number and thirty-one is one hundred thirteen. write the equation as n-31=113 and subtract 31 from both sides. the answer is 82. write the equation as n+31=113 and subtract 31 from both sides. the answer is 82. write the equation as n+31=113 and add 31 to both sides. the answer is 144. write the equation as n-31=113 and add 31 to both sides. the answer is 144.

Find the value of x that will make l ll m

You are saving to buy a bicycle; so far you save 55.00. the bicycle costs 199.00. you earn 9.00 per hour at your job. which inequality represents the possible number of h hours you need to work to buy the bicycle?