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1. Let L be a lattice in R[tex]^n[/tex] and g and <I think “and” should be “an” here?> element of E(n). Show that g maps L onto L if and only if gx and g[tex]^-^1[/tex]x are in L for each x in L.

2. Show that (A,b) is a symmetry of the lattice L if and only if b is in L, and A is in the holohedry of L.

3.Show that the set of squares in Sn is a subgroup for n = 2,3,4,5.