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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20220228T081148Z
DTSTART:20220308T130000Z
DTEND:20220308T140000Z
SUMMARY:Manchester Algebra Seminar - John MacQuarrie
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}v15v-kz742y
05-f84qec
DESCRIPTION:Speaker: John MacQuarrie - Universidade Federal de Minas Gera
is\n\nTitle: A variant of a theorem of Weiss characterising permutation
modules\n\nAbstract: In 1988\, Weiss gave a powerful sufficient conditio
n guaranteeing that a lattice U for a finite p-group G over the p-adic i
ntegers be a permutation module\, in terms of modules for groups smaller
than G. Weiss' Theorem is not a characterization\, however. Working w
ith Pavel Zalesski\, we give a characterization of permutation Z_pG-modu
les for a finite p-group G. The theorem has the form: "U is a permutati
on module if\, and only if\, the G/N-modules A\, B and C are permutation
modules". Easy (rank 3) examples show that one cannot remove the deman
ds on A or B from the theorem\, but we didn't know if the final conditio
n is redundant. Working with Marlon Stefano\, we show that we cannot re
move this condition\, by constructing a non-permutation lattice such tha
t A and B are permutation modules. The methods used to construct the ex
ample are interesting in their own right\, utilizing an ingenious descri
ption of ZpG-lattices (G abelian) due to Butler. I'll explain all this.
\n\n\nPlace: Frank Adams (and to be streamed online*)\n\n*subject to equ
ipment and connection\n\nTea and biscuits 12:45 in the foyer
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams\, Alan Turing Building\, Manchester
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