ass3_2 - 3) Let D (the innite dihedral group) be the...

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MATH 335 001 Computational Algebra Winter 2006 Assignment 3.2 GROUPS 1) Use Tietze transformations to show that the group G = h x,y,z | ( xy ) 2 xy 2 i . is a free group of rank 2. 2) Show that the groups given by the following presentations h x,y,z | x = yzy - 1 ,y = zxz - 1 ,z = xyx - 1 i , h x,y | xyx = yxy i , h a,b | a 3 = b 2 i are isomorphic (obtainable from each other by Tietze transformations).
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Unformatted text preview: 3) Let D (the innite dihedral group) be the multiplicative group of 2 2 matrices of the form k 0 1 where { 1 ,-1 } ,k Z . Show that D can be presented by h x,y | x 2 = 1 ,x-1 yx = y-1 i ....
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