Functor categories for groups
Friday 4 April 2025. Hybrid: Lancaster, Postgraduate Statistics Centre Lecture Theatre A54 and Zoom.
Provisional timetable (UK times)
13:30-13:30 John Nicholson (Glasgow)
14:30-15:30 Simon Smith (Lincoln)
15:30-16:00 break
16:00-17:00 Clover May (Trondheim)
Titles and abstracts
John Nicholson: The cancellation property for projective modules over integral group rings
Let G be a finite group and let Z[G] denote the integral group ring. If two finitely generated projective Z[G]-modules P and Q are isomorphic after taking a direct sum with the free module Z[G], are they necessarily isomorphic? If so, we say that Z[G] has the cancellation property. This was studied extensively in the 1960s-80s by H. Jacobinski, A. Fröhlich and R. G. Swan, and has applications both in number theory and algebraic topology. However, a complete classification of the finite groups which have the cancellation property has remained out of reach.
In this talk, I will present a new cancellation theorem for projective Z[G]-modules and explain how this leads to an approach to complete the classification using only finite computation. By utilising recent computer calculations of W. Bley, T. Hofmann and H. Johnston, this leads a classification of when cancellation occurs among all finite groups G which have no quotient which is a binary tetrahedral group, binary octahedral group, or a binary icosahedral group.
Simon Smith: nearer the time
Clover May: nearer the time
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More information on the Functor Categories for Groups see the website: Functor Categories for Groups
To register for the event or to receive the talk links, please email the organiser Nadia Mazza (n.mazza@lancaster.ac.uk).
The FCG Research Group is supported by an LMS Joint Research Groups in the UK Scheme 3 grant. Current corresponding organisers for this are Dawid Kielak (Oxford), Nadia Mazza (Lancaster) and Simon Smith (Lincoln). Limited funding is available for PhD students, allocated on a first come first served basis.
For UK-based mathematicians with caring duties the LMS has a Caring Supplementary Grant scheme which allows participants of meetings like ours to apply for help covering caring costs. See London Mathematical Society grants for other funding possibilities.
