Ammu Elizabeth Antony
Title: Structural results on Non-Abelain Tensor Product and Applications Abstract: We study different conditions under which the short exact se-quence 0 → ∇(G) → G ⊗ G → G ∧ G → 0 splits. We will also be giving some applications for our results.
Harsha Arora Title: What is the probability of an automorphism fixes a group element? Abstract: Extending the notion of probability to the automorphism of a group, we find the probability of an arbitrarily chosen automorphism of a group fixing an arbitrary element of the group.
Anirban Bose
Title: On the genus number of algebraic groups Abstact: In this presentation we shall describe a method of computing the number of orbit types for simply connected simple algebraic groups over an algebraically closed field as well as for compact simply connected Lie groups.
Sumana Hatui Title: A characterization of finite $p$-groups by their Schur multiplier Abstract: Let $G$ be a finite $p$-group of order $p^n$ and $M(G)$ be its Schur multiplier. It is well known result by Green that $|M(G)|= p^{\frac{1}{2}n(n-1)-t(G)}$ for some $t(G) \geq 0$. In this article we classify non-abelian $p$-groups $G$ of order $p^n$ for $t(G)=\log_p(|G|)+1$.
Dilpreet Kaur
Title: Wedderburn Decomposition of Real Special 2-groups Authors: Amit Kulshrestha Abstract: Let G be a real special 2-group. In this poster, our aim is to provide an algorithm for explicit computation of Wedderburn decomposition of rational group algebra Q[G]. Our approach uses quadratic maps associated to special 2-group.
Surinder Kaur Title: Units in commutative group ring over polynomial ring Authors: Manju Khan and Surinder Kaur Abstract: Let G be a group and R be a ring. The group ring RG is the set of all formal linear combinations Σg∈G agg with ag = 0 for all but finitely many g ∈ G. In the poster, I will present the structure of the normalized unit group V (F[x]G) of the modular group ring F[x]G where F[x] is a univariate polynomial ring over a field F of characteristic p and G is a finitely generated abelian group whose torsion subgroup is a p-group.
Rahul Kitture
Title: Non-abelian groups with abelian group of automorphisms Abstract: Does there exists a non-abelian group with abelian automorphism group? This question was raised by Harold Hilton in his book "An Introduction to the Theory of Groups of Finite Order" (1908). G. A. Miller showed that there exists such a group of order 64, hence such groups are now also termed as "Miller groups". Since then, several examples of Miller groups have been constructed, and among them, many groups are special p-groups. Andreas Caranti (2015) described a simple module theoretic approach to construct an infinite family of Miller groups from a single Miller p-group with some restrictions. In a joint work with Manoj Yadav, we noticed that there is a little gap in the methods which may not ensure that the constructed groups are Miller, and we tried to fill the gap in the methods. The poster will include a survey on study of Miller groups with focus on Caranti's module theoretic approach.
Tushar Kanta Naik
Title: Classification of p-groups of conjugate type {1, p^3} upto isoclinism Abstract: A finite group G is said to be of conjugate type {m1 , m2 , . . . , mn }, if the set of conjugacy class sizes of G is {m1 , m2 , . . . , mn }. Finite groups of conjugate type {1, n} were first investigated by Ito in 1953. He proved that if G is of conjugate type {1, n}, then n is a power of some prime p and G is a direct product of a non-abelian Sylow p-subgroup and an abelian p-subgroup; in particular G is nilpotent. Hence, to understand such groups, it is sufficient to study finite p-groups of conjugate type {1, p^n } for n ≥ 1. Half a century later, Ishikawa proved that finite p-groups of conjugate type {1, p^n } can have nilpotency class at most 3. In a different paper, he classified p-groups of conjugate type {1, p} and {1, p^2} upto isoclinism. In a joint work with Dr. Manoj Kumar, we investigate finite p-groups of conjugate type {1, p^3} and classify them upto isoclinism. Surprisingly we found that such groups can not be of nilpotency class 3.
Karimilla Bi Nayeem
Title: Residues Modulo Powers of Two in the Young-Fibonacci Lattice Authors: Amritanshu Prasad and P.Giftson Abstract: The Young-Fibonacci graph is a graded graph Y whose n th-row con- sists of words in the alphabet {1, 2} which sum up to n. For each node x of this graph, let fx denote the number of geodesic paths from the unique node in its first row to x. The subgraph induces in Y by the vertices x such that fx is odd is known to be a binary tree, called the Macdon- ald tree. We give a recursive description of the Macdonald tree when its nodes are labelled by their f-numbers. We show that the residues of the f-numbers modulo powers of 2 are eventually equidistributed.
Pradeep Kumar Rai Title: On the order of the Schur multiplier of finite p-groups
Abstract: We derive some bounds on the order of the Schur multiplier of finite p-groups refining earlier known bounds. As an application we classify finite p-groups of nilpotency class 2 having Schur multiplier of maximum order. Finally we try to find Schur multiplier and covering groups of special p-groups having derived subgroup of maximum order. This gives an answer to a question of Berkovich.
Asif Shaikh Title: Zeta functions of finite Schreier graphs and their zig-zag products Abstract: We investigate the Ihara zeta functions of finite Schreier graphs Γn of the Basilica group. We show that Γ1+n is 2 sheeted unramified nor-mal covering of Γn, for all n ≥ 1 with Galois group Z /2Z . In fact, for any n > 1, r ≥ 1 the graph Γn+r is 2n sheeted unramified, non normal cov- ering of Γr. In order to do this we give the definition of the generalized replacement product of Schreier graphs of Basilica group. We also show the corresponding results in zig-zag product of Schreier graphs Γn with a 4-cycle.
