Seminario / Isaacs
The Ischia Group Theory 2020 Conference
was planned for 30 March - 4 April 2020. It has now been postponed.
In the meantime, we are offering a series of online lecture
by leading researchers (https://sites.google.com/unisa.it/e-igt2020/).
TIME: September 24th, 2020 18:00 CEST (UTC+2)
COFFEE BREAK: The talk will start at 18:00 CEST.
The conference room will open at 17:45 CEST for a coffee break
- Bring Your Own tea/coffee mug - biscuits appreciated -
and join us for some smalltalk before the event.
SPEAKER: I. Martin Isaacs (University of Wisconsin at Madison)
TITLE: Carter subgroups and characters
ABSTRACT: A Carter subgroup is a self-normalizing nilpotent
subgroup, and a theorem of Carter asserts that
every solvable group contains a unique conjugacy
class of Carter subgroups.
Given a solvable group G with Carter subgroup C,
we construct a family of injective maps from the
set of linear characters of C into the set Irr(G).
There are usually many maps in this family, but
all of them have exactly the same image. This
common image is thus a canonically determined set
of irreducible characters of G, and we refer to
the members of this set as the "head characters"
of G. They are characterized by their behavior
with respect to the C-composition series of G.
Each head character of G has degree dividing
|G:C|, and each of them restricts irreducibly to
the nilpotent residual of G. Experiment suggests
that the head characters of G are exactly those
irreducible characters that have nonzero values
on all elements of C, but this remains unproved.
The organising committee of the Ischia Online Group Theory Conference
(GOThIC) is inviting you to a scheduled Zoom meeting.
- The TIME OF THE TALK is 18:00 CEST.
- The Zoom link is NEW.
- You are welcome to share the Zoom link with other interested
parties, but PLEASE DO NOT POST THE LINK PUBLICLY.
- When joining, please MAKE SURE THAT YOUR NICKNAME IS YOUR NAME AND
SURNAME, or close to it, so that the organisers can recognise you
and let you in