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1. (a) Let G be a group and consider the power set P(G) = {SCG) Explicitly verify that GXP(G) + P(G) (9,8) gSg-1 = {gsg- S ES

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1. (a) Let G be a group and consider the power set P(G) = {SCG) Explicitly verify that GXP(G) + P(G) (9,8) gSg-1 = {gsg- S ES

solutions ANDE G is group acting on s= P(G) ax P(G) > P(G) defined by (g.is) -s gsg. Now gsgro į {gsg: ses} for each SEG ,(6) Andre G = S5 S= < (113) (2:51) = {(1,3)(2,5), e} (9,5)= { g (43) (3.5)9*, geg? - $9 (1,3) (2,519, e} [ (1,3) (2,5)} =

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