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Abstract: All groups have 2 generators. For every prime power q, the GeneralizedBurnside Theorem Theorem GB produces an infinite number of solvable groups,Some, such as groups of a prime power exponent, have only elements of finiteorder and are therefore finite groups. Others have elements of infinite orderand are thus infinite groups.All these groups, even when infinite, are closely related to groups ofexponent q. They have at least one generator of order q, and their commutatorsubgroup has exponent q.

Autor: S. Bachmuth


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