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(a) Determine a linearly independent subset of G which generates G as an abelian group (b) Show that Z4/G is a free abelian group and determine its rank Solution (b) The linear map Z4 7→Z,(x,y,z,w) 7→2x3y 5z 7w has kernel G, and is onto because 2 and 3 are relatively prime Hence Z4/G is isomorphic. If you don't, your new dictionaries won't be recognized (eg it will use only LocalSpellingWords) Another possible cause of problems is that you did not place the dictionaries in the ''active'' "MoinMoin" package directory, ie the one that is actually imported by your CGI script PK z“qB¬ €³BB 2## Please edit system and help pages. Nov 17, 11 · that n is, in fact, the order of g1 xg we know no smaller m works for x, but g1 xg, isn't x, it's some other element of G, so you need to prove no smaller m will work for g1 xg suppose (as an imaginary example) that g1 xg = x 2, and x = 4 then g1 xg would have order 2, and so would still be e if raised to the 4th power since e 2 = e do not confuse the statements x n.

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