[Turkmath:380] Gebze Technical University, Department of Mathematics Colloquium

[Tülay Yıldırım]

Sayin Liste Uyeleri,

GTU Matematik Bölümü Genel Seminerleri kapsamında,
03 Nisan Cuma günü saat 14:00'da Ayşe BERKMAN
(Mimar Sinan Universitesi) bir seminer  verecektir. Seminerin
detayları aşağıda olup tüm ilgilenenler davetlidir.

Saygılarımızla,

Title: Sharply 2-Transitive Group Actions

Abstract:
A typical example of a sharply 2-transitive action is the action of the group of affine transformations of a field. In fact, for this example, we do not need all the field axioms, working over a “near field” is sufficient. This is the so-called standard sharply 2-transitive group. In 1936, Zassenhaus proved that all finite sharply 2-transitive groups are standard. In 1952, Tits extended this result to locally compact connected groups. Later, more results from different authors came verifying that under certain assumptions a sharply 2-transitive group is standard. However, the general problem of whether any sharply 2-transitive group is standard or not, remained open until 2014, when Rips, Segev and Tent, constructed the first non-standard example of a sharply 2-transitive group, and answered the almost a century-old problem negatively. Quickly after that, again in 2014, Tent and Ziegler constructed a much easier example. However, all these examples are of permutation characteristic 2 and none of them is of finite Morley rank. Therefore, there are still many open questions related to the subject.

In my talk, I am planning to review the history and fundamental results in the area, then talk about the Tent-Ziegler example, and finally mention some old and new results in the finite Morley rank context.




Dear all,

There will be a seminar in Gebze Technical University (GTU) on 3th of
April by Ayşe BERKMAN (Mimar Sinan Uni)
Time  and  place:  March 27th, at 14:00 in Department of Mathematics,
Building I, Seminar room.

Title: Sharply 2-Transitive Group Actions

Abstract:
A typical example of a sharply 2-transitive action is the action of the group of affine transformations of a field. In fact, for this example, we do not need all the field axioms, working over a “near field” is sufficient. This is the so-called standard sharply 2-transitive group. In 1936, Zassenhaus proved that all finite sharply 2-transitive groups are standard. In 1952, Tits extended this result to locally compact connected groups. Later, more results from different authors came verifying that under certain assumptions a sharply 2-transitive group is standard. However, the general problem of whether any sharply 2-transitive group is standard or not, remained open until 2014, when Rips, Segev and Tent, constructed the first non-standard example of a sharply 2-transitive group, and answered the almost a century-old problem negatively. Quickly after that, again in 2014, Tent and Ziegler constructed a much easier example. However, all these examples are of permutation characteristic 2 and none of them is of finite Morley rank. Therefore, there are still many open questions related to the subject.

In my talk, I am planning to review the history and fundamental results in the area, then talk about the Tent-Ziegler example, and finally mention some old and new results in the finite Morley rank context.

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