2 Let T be a rectangle (not a square) and G = Sym(T) the symmetry group...

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2 Let T be a rectangle (not a square) and G = Sym(T) the symmetry group of T. (i) Show that |G|= 4. (ii) Find all elements of G, describing them geometrically. (iii) Show that you can find two elements of G so that every element of G can be written in terms of these two. Find a normal form for elements of G. (iv) Write down a presentation for G with these two generators, explaining why you have found enough relations. 2 Let T be a rectangle (not a square) and G = Sym(T) the symmetry group of T. (i) Show that |G|= 4. (ii) Find all elements of G, describing them geometrically. (iii) Show that you can find two elements of G so that every element of G can be written in terms of these two. Find a normal form for elements of G. (iv) Write down a presentation for G with these two generators, explaining why you have found enough relations.