The Structure of Torsion Abelian Groups given by Presentations by Peter Crawley and Alfred W, Hales
نویسنده
چکیده
If each of the elements in R involves only one generator in X, then G(X, R) is a direct sum of cyclic groups. On the other hand, if G is any abelian group, then GÇ=G(X, i?), where each element in R involves at most three generators in X; indeed this isomorphism results if we take X = G and R equal to the set of all elements in F o of the form x+y~ z, where z = x+y in G. Our purpose here is to investigate the structure of the group G(X, R) in the intermediate case when each of the elements of R involves at most two generators, and G(X, R) is a torsion group. We can evidently restrict our attention to ^-groups, and in this case it is easily seen that G(X, R)=G(X', i?')> where each element in R' is of one of the forms px or px — y.
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