This article examines lower bounds for the representation growth of finitely generated (particularly profinite and pro-p) groups. It also considers the related question of understanding the maximal multiplicities of character degrees in finite groups, and in particular simple groups.

In this paper, ‘T’ character-type array antenna system is proposed which estimates the directions of arrival (DOA) by the virtual uniform rectangular arrays. The proposed system consists of 4 antenna elements distributed like the character ‘T’. The performance of the proposed system in DOA estimation is evaluated by some simulation and experiments. First we show that DOA is estimated correctly ...

For a finite group G, let cd(G) be the set of irreducible complex character degrees of G forgetting multiplicities and X1(G) be the set of all irreducible complex character degrees of G counting multiplicities. Suppose that p is a prime number. We prove that if G is a finite group such that |G| = |PGL(2, p)|, p ∈ cd(G) and max(cd(G)) = p+1, then G ∼= PGL(2, p), SL(2, p) or PSL(2, p) × A, where ...

Let S be a finite set of powers of p containing 1. It is known that for some choices of S, if P is a finite p-group whose set of character degrees is S, then the nilpotence class of P is bounded by some integer that depends on S, while for some other choices of S such an integer does not exist. The sets of the first type are called class bounding sets. The problem of determining the class bound...

This paper proves the following conjecture of Boyer and Zhang: If a small hyperbolic knot in a homotopy sphere has a non-trivial cyclic surgery slope r, then it has an incompressible surface with non-integer boundary slope strictly between r − 1 and r + 1. I state this result below as Theorem 4.1, after giving the background needed to understand it. Corollary 1.1 of Theorem 4.1 is that any smal...

In this paper we prove some mainly asymptotic results concerning the irreducible character degrees of .nite groups of Lie type. Applications are given to the study of the mixing time of random walks on these groups, with certain conjugacy classes as generating sets. In various situations we show that the mixing time is 2; this seems to be the .rst determination of an exact bounded mixing time f...

We prove that a knowledge of the character degrees of a finite group G and of their multiplicities determines whether G has a Sylow p-subgroup as a direct factor. An analogous result based on a knowledge of the conjugacy class sizes was known. We prove variations of both results and discuss their similarities.

Abstract Handwritten text recognition systems interpret the scanned script images as composed of letters. In this paper, efficient offline methods using fuzzy degrees, well interval degrees type-2, are proposed to recognize letters beforehand decomposed into strokes. For such strokes, first stage used create a set hypotheses whether group strokes matches letter or digit patterns. Subsequently, ...

1. Introduction. Let G be a finite group and, as usual, write cd(G) to denote the set of degrees of the irreducible characters of G. This set of positive integers encodes a great deal of information about the structure of G, and we mention just a few of the many known results of this type. If G is nilpotent (or more generally, if G is an M-group), a result of K. Taketa asserts that the derived ...