Genus of a pullback
Date
2021
Authors
Tonisi, Thandile
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Let Q be a finitely generated nilpotent group. The Mislin genus G (Q)
is defined to be the set of isomorphism classes of finitely generated
nilpotent groups R such that for every prime p, the p-localizations Rp
and Qp are isomorphic. If the group Q has a finite commutator sub group, the genus admits an abelian group structure. In this work, we
study the Mislin genus of nilpotent groups through pullbacks. For a
relatively prime pair of natural numbers (n, u), let Q = hx, y | x
n =
1, yxy−1 = x
u
i, where Q is a pullback. We compute the genus G (Q)
and we investigate the relationship between the genera of these nilpo tent groups.
Description
A dissertation submitted in fulfilment of the requirements for the degree of Master of Science (Mathematics) to the Faculty of Science, School of Mathematics, University of the Witwatersrand, Johannesburg, 2021