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Hi, i am trying to find cosets of S_3 in Maple. I have done this so far: > restart; > with(group); > S_3 := permgroup(3, {[[1, 2]], [[1, 2, 3]], [[2, 3]], [[1, 3]], [[1, 3, 2]]}); permgroup(3, {[[1, 2]], [[1, 2, 3]], [[2, 3]], [[1, 3]], [[1, 3, 2]]}) > grouporder(S[3], ident); Error, (in group:-grouporder) expecting a permgroup or a grelgroup, but received S[3] > Group order should be 6 (which is 3!) but for some reason it does not work. Also I am getting an error message when I try to find cosets of S_3. > ident := permgroup*(3, {[]}); > cosets(S_3, ident); Error, (in group:-cosets) invalid arguments I have also tried to find y-cosets of g (where y is a subgroup) using the following: > with(group); g := grelgroup({1, 2, 3}, {[1, 2], [1, 2, 3], [2, 3], [1, 3], [1, 3, 2]}); cosets(subgrel({y = ([1, 3])}, g)); {[]} > where g = S_3 and y={1, (13)} (y is a subgroup of g). any help would be appreciated! many thanx.

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