[Turkmath:5314] Yeditepe Mathematics Department 25th Year Seminars, December 17, 2021; by Gülin Ercan (METU)

[Mehmet Akif Erdal]

Dear list members,

You are most cordially invited to Yeditepe Mathematics Department 25th Year
Seminars. The details of this week's talk are as follows.

Speaker: Gülin Ercan (Middle East Technical University)

Title: Good Action,

Abstract: Let $G$ be a group acted on by a group $A$ by automorphisms. The
nature of this action is very restrictive and hence informative about the
structure of $G$. We have
been carrying on research in this area, especially on length type problems,
in several
collaborated works over the years. The action is said to be coprime if $G$
and $A$ have
coprime orders. The existence of nice conditions which are valid in this
case made
it almost traditional to assume that the action is coprime. After many
attacks to a
longstanding noncoprime conjecture we have recently introduced the concept
of a
good action of $A$ on $G$ in a joint work with Güloğlu and Jabara. We say
the action
is “good” if $H = [H, B]C_H(B)$ for every subgroup $B$ of $A$ and for every
$B$-invariant
subgroup $H$ of $G$. It can be regarded as a generalization of the coprime
action due
to the fact that every coprime action is good and there are noncoprime
actions
which are good. It is expected that this concept may help to understand the
real
difficulties in studying a noncoprime action. We have achieved extending
several
coprime results to good action case. With this talk I aim to present a
review of
our results and discuss the main difficulties that arise in the study of a
noncoprime
good action.


Date: Friday, December 17, 2021
Time: 16:00
Zoom Meeting ID: 889 3945 0567
Passcode: 7tpSeminar

----

Değerli liste üyeleri,

Yeditepe Matematik Bölümü 25. Yıl Seminerleri kapsamında bu hafta yapılacak
olan seminerin detayları aşağıdaki gibi olup tüm ilgilenenler davetlidir.

Konuşmacı: Gülin Ercan (Middle East Technical University)

Başlık: Good Action

Özet: Let $G$ be a group acted on by a group $A$ by automorphisms. The
nature of this
action is very restrictive and hence informative about the structure of
$G$. We have
been carrying on research in this area, especially on length type problems,
in several
collaborated works over the years. The action is said to be coprime if $G$
and $A$ have
coprime orders. The existence of nice conditions which are valid in this
case made
it almost traditional to assume that the action is coprime. After many
attacks to a
longstanding noncoprime conjecture we have recently introduced the concept
of a
good action of $A$ on $G$ in a joint work with Güloğlu and Jabara. We say
the action
is “good” if $H = [H, B]C_H(B)$ for every subgroup $B$ of $A$ and for every
$B$-invariant
subgroup $H$ of $G$. It can be regarded as a generalization of the coprime
action due
to the fact that every coprime action is good and there are noncoprime
actions
which are good. It is expected that this concept may help to understand the
real
difficulties in studying a noncoprime action. We have achieved extending
several
coprime results to good action case. With this talk I aim to present a
review of
our results and discuss the main difficulties that arise in the study of a
noncoprime
good action.

Tarih: 17 Aralık 2021, Cuma
Saat: 16:00
Zoom Meeting ID: 889 3945 0567
Passcode: 7tpSeminar


Listing: https://researchseminars.org/seminar/7tepemathseminars
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