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CATEGORIES:Algebra seminar
SUMMARY:Products of finite nilpotent groups - John Cossey
(Canberra
DTSTART:20120510T150000Z
DTEND:20120510T160000Z
UID:TALK2594AT
URL:/talk/index/2594
DESCRIPTION:Suppose _A_ and _B_ are subgroups of a group _G_.
We say that _G_ is the product of _A_ and _B_ if _
G_=_AB_={_ab_ : _a_ ∈ _A_\, _b_ ∈ _B_}. A natural
question to ask is whether\nproperties of _G_ can
be deduced from properties of _A_ and _B_. There i
s an extensive literature on this question. Many p
roperties have been considered- see for example th
e book of Amberg\, Franciosi and de Giovanni and t
hat of Ballester-Bolinches\, Esteban-Romero and As
aad.\n\nMany results concentrate on the case of _A
_ and _B_ nilpotent. Most results are\naimed at re
stricting the structure of non-nilpotent products
_G_\; for example\, under appropriate restrictions
\, _G_ will be supersoluble. However very little i
s known about the structure when _G_ is itself nil
potent.\n\nIf _G_ is nilpotent\, there are many in
variants we could consider: derived length\, class
\, coclass\, breadth and rank as examples. Very li
ttle is known about any of these. I will describe
what is known.
LOCATION:Watson Building\, Lecture Room A
CONTACT:David Craven
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