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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20221122T160038Z
DTSTART:20221129T130000Z
DTEND:20221129T140000Z
SUMMARY:Manchester Algebra Seminar - Leo Margolis
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}slf-la6oaao
u-81ikg6
DESCRIPTION:Speaker: Leo Margolis\n\nTitle: Units in group rings and rep
resentation theory of C_p\n\nAbstract: The unit group U(ZG) of the integ
ral group ring ZG of a finite group G is a long studied object\, but nev
ertheless many fundamental questions remain open. The strongest possible
expectation on finite subgroups of U(ZG)\, expressed by Zassenhaus\, ha
d been that these always lie inside the trivial units Â±G up to conjugati
on in the bigger group algebra QG. While this has been refuted in this m
ost general form\, it is still open for p-subgroups\, and also whether t
he order of elements in U(ZG) coincide with those in G remains unknown (
after a suitable normalisation process). \nI will explain a method which
has been used to achieve several results on these questions\, but the b
ottle neck of which\, for the moment\, is the understanding of represent
ations of the most simplest groups one can imagine - the cyclic groups o
f prime order p. Overcoming some of these difficulties\, recent progress
allows us to show that Zassenhausâ€™ question has a positive answer at le
ast for units of order p\, when the Sylow p-subgroup of G is also assume
d to be of prime order.\nThis is joint work with Florian Eisele.\n\n\nPl
ace: Frank Adams (this term the seminar will not be streamed online)\n\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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