seminars:alge

Unless stated otherwise, the seminar meets Tuesdays in room WH-100E at 2:50 p.m. There will be refreshments served at 4:00 in room WH-102.

Organizers: Ben Brewster and Fernando Guzmán

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**January 24**

Ben Brewster (Binghamton University)

*The Frattini subgroup*

: The Frattini subgroup of group G (denoted Fr G ) is defined as the intersection of all the maximal subgroups of G. If G has no maximal subgroups, the standard device is that G = Fr G. This talk will be concerned primarily with non-trivial finite groups and so this standard device is not relevant.*Abstract*- The Frattini subgroup is called by the name of its originator in 1885. It is analogous to the Jacobson radical in ring theory and it can be generalized to various posets.
- I will present some examples and basic results about the Frattini subgroup. It has many different uses in Group theory. I will choose a few and give some examples, but then tackle the question of which groups G can be Fr H for some H.
- Speaking now about finite groups, it turns out the Frattini subgroup is nilpotent, every finite abelian group is isomorphic to the Frattini subgroup of an abelian group, but no non-abelian group of order p^3 is isomorphic to the Frattini subgroup of any group.
- I am unaware of the classification of groups G such that G is isomorphic to Fr H for some H.

**January 31**

Speaker (School)

*Title*

:*Abstract*

**February 07**

Matt Evans (Binghamton University)

A Structure Theorem for BCK-algebras*Title*

:*Abstract*BCK-algebras were introduced in the 1960's as models for set difference and implicational calculus. In this talk I will define BCK-algebras and provide some examples before I restrict to the variety of bounded commutative BCK-algebras. Then I will classify all finite bounded commutative BCK-algebras (up to isomorphism).

**February 14**

Speaker (School)

*Title*

:*Abstract*

**February 21**

Dikran Karagueuzian (Binghamton University)

*Title : Randomness of Polynomials over Finite Fields*

:*Abstract: A polynomial over a finite field may be compared to a random map from the finite field to itself. The extent to which this comparison is valid comes up in the analysis of some primality testing algorithms. Martins and Panario have results on the validity of the comparison for generic polynomials, and we are able to generalize some of these results, including specifically their result on the coalesence, to non-generic polynomials. This is joint work with Per Kurlberg.*

**February 28**

Joe Cyr (Binghamton University)

A Structure Theorem for Entropic Quandles*Title*

: Entropic Quandles form a large subclass of binary modes. In this talk I will introduce this algebra and develop a representation of them using a blend of affine structures.*Abstract*

**March 07**

*Winter Break*

**March 14**

Adam Allan (C.C.S.U.)

*Symmetry of Endomorphism Algebras*

:*Abstract: In this talk we will consider the problem of determining whether the endomorphism algebra of a prescribed module is symmetric. In particular,we will focus on the examples of indecomposable modules for the dihedral 2-groups.*

**March 21**

Speaker (School)

*Title*

:*Abstract*

**March 28**

Hung Tong-Viet (Kent State University)

*Derangements in permutation groups*

: A*Abstract***derangement**(or fixed-point-free permutation) is a permutation with no fixed points. One of the oldest theorems in probability, the Montmort limit theorem, states that the proportion of derangements in finite symmetric groups $\textrm{S}_n$ tends to $e^{-1}$ as $n$ approaches infinity. A classical theorem of Jordan implies that every finite transitive permutation group of degree greater than $1$ contains derangements. This result has many applications in number theory, game theory and representation theory. There are several interesting questions on the number and the order of derangements that have attracted much attention in recent years. In this talk, I will discuss some recent results on primitive permutation groups with some restriction on derangements (joint with T.C. Burness).

**April 04**

Eran Crockett (Binghamton University)

*Nilpotence vs supernilpotence*

: In universal algebra there are two different notions of nilpotence that happen to coincide for groups. I will describe the relation between the nilpotence class of an algebra and the maximum supernilpotence class of the algebra's congruences.*Abstract*

**April 11**

*Spring Break*

**April 18**

Phillip Wesolek (Binghamton University)

*Elementary Groups*

: In the study of totally disconnected locally compact (tdlc) groups, groups “built by hand” from compact groups and discrete groups frequently arise. In particular, such groups arise as obstructions to general theorems. To isolate these groups, we consider the class of elementary groups: The smallest class of tdlc groups which contains the profinite groups and discrete groups and is closed under the elementary operations.In this talk, we explore this class, showing that it is very robust. We conclude by posing several open questions, including a conjectural connection with elementary amenable groups.*Abstract*

**April 28**

Speaker (School)

*Title*

: TBD*Abstract*

**May 02**

Ben Steinberg (C.C.N.Y.)

*Title*

: TBD*Abstract*

seminars/alge.txt · Last modified: 2017/03/20 13:52 by ben