Solvable matrix groups and the Burnside problem

Details Solvable matrix groups and the Burnside problem Solvable matrix groups and the Burnside problem

2006-09-14

arxiv.org/abs/math/0609415v1

Mathematics

Group Theory

14 pages. Section 5, which is 3 pages, has been completely rewritten in an effort to make it simple and clear; no background,

Scientific paper

All groups are 2-generator. For any prime-power q, Theorem 1 constructs a solvable matrix group over a quotient of a Laurent polynomial ring. This group is closely related to a group of exponent q as shown in Theorems 2 & 3 . Theorem 4 in section 5 shows that a group of prime-power exponent contains the relations of a solvable group. It follows that the Burnside groups of exponent q are solvable, and it is easy to deduce that the solvability class of these groups tends to infinity with q. Crucial to this work, especially for precise bounds on the solvability class, is an earlier paper with Heilbronn and Mochizuki.

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