Başlık: (Counter) examples in Group Theory
Eğitmen: Ayşe Berkman
Kurum: MSGSÜ
Tarih: 3-9 Şubat 2020
Önkoşul: Standard undergraduate level of group theory (Symmetric and alternating groups, dihedral groups, Lagrange Theorem, quotient groups, isomorphism theorems, direct products, Sylow Theorems, classification of finite abelian groups).
Seviye: Advanced Undergraduate and Graduate
İçerik: In the first half of the course, counterexamples will be discussed, to more or less standard statements, such as
* All non-abelian groups have even order.
* Subgroups of a finitely generated group are also finitely generated.
* If the orders of elements of two finite groups match then the groups are isomorphic.
In the first part of the course, students are expected to present their counterexamples at the board.
In the second half, depending on the students’ interests, more famous but also more difficult groups will be studied. Examples may include Tarski monsters, Grigorchuk group, Hall’s universal group, a non-split sharply 2-transitive group.

During the course, tools to construct new groups (such as semidirect products, wreath products, HNN extensions, direct and inverse limits) will also be presented.