Question

Abstract Algebra

Exercise 4.2.3 Edges e, e of a tetrahedron T are said to be opposite if they a vertex). The 6 edges can be partitioned into a set X of three pairs of opposite edges. Prove that Gs, the group of symmetries of T, acts on X and the kernel K<G, is a normal subgroup of order 4 disjoint (that is, they do not share are a normal subgroup of Gs S (and (1) and S, of The previous exercise is interesting in that it provides a geometric description of different than A. It turns out that for any n 4, the only normal subgroup of S is A course)

Answer 1

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ANSWER:

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