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Title: The D(2)-problem for some metacyclic groups
Author: Vittis, Jason Marcus
ISNI:       0000 0004 8508 1726
Awarding Body: UCL (University College London)
Current Institution: University College London (University of London)
Date of Award: 2019
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We study problems relating to the D(2)-problem for metacyclic groups of type G(p,p-1) for p an odd prime. Specifically we build on J Nadim's work, which showed that over the integral group ring of G(5,4), the module of integers (upon which the group acts trivially) admits a diagonal resolution and a minimal representative for the third syzygy is R(2)+[y-1). Motivated by this result, we show that R(2)+[y-1) is both full and straight over the integral group ring of G(p,p-1) where p is any odd prime. Given FEA Johnson's work on the D(2)-problem, this immediately leads to the conclusion that G(5,4) satisfies the D(2)-property, as well as providing a sufficient condition for the D(2)-property to hold for G(p,p-1), namely the condition that R(2)+[y-1) is a minimal representative for the third syzygy. Following this result, we prove a theorem, which in tandem with work from FEA Johnson relating to the module R(2) significantly simplifies the calculations required to show that R(2)+[y-1) is a minimal representative for the third syzygy. Finally, we carry out these calculations for the group G(7,6) and prove that G(7,6) satisfies the D(2)-property.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available