Related papers: Some results on capable groups of prime exponent a…

Let p be a prime larger than 3 and let G be a finite group. We prove that G is p-solvable of p-length at most 2 if there are at most two distinct character degrees relatively prime to p in the principal p-block of G. This generalizes a…

We give a complete list of the class two groups with exponent $p$ and order dividing $p^8$. For each group in the list we compute the number of immediate descendants of order $p^9$ with exponent $p$. In each case the number of descendants…

For the hyperelliptic curve C_p with equation y^2=x(x-2p)(x-p)(x+p)(x+2p) with p a prime number, we discuss bounds for the rank of its Jacobian over Q, find many cases having 2-torsion in the associated Shafarevich-Tate group, and we…

We show that certain $p$-adic Eisenstein series for quaternionic modular groups of degree 2 become "real" modular forms of level $p$ in almost all cases. To prove this, we introduce a $U(p)$ type operator. We also show that there exists a…

Let $G$ be a finite group and assume $p$ is a prime dividing the order of $G$. Suppose for any such $p$, that every two abelian $p$-subgroups of $G$ of equal order are conjugate. The structure of such a group $G$ has been settled in this…

In this article new cases of the Inverse Galois Problem are established. The main result is that for a fixed integer n, there is a positive density set of primes p such that PSL_2(F_{p^n}) occurs as the Galois group of some finite extension…

This note deals with the computation of the factorization number $F_2(G)$ of a finite group $G$. By using the M\"{o}bius inversion formula, explicit expressions of $F_2(G)$ are obtained for two classes of finite abelian groups, improving…

In this paper we present new examples of simple $p$-local compact groups for all odd primes. We also develop the necessary tools to show saturation, simpleness and the non-realizability as $p$-compact groups or compact Lie groups, which can…

The complete classification of the finite simple groups that are $(2,3)$-generated is a problem which is still open only for orthogonal groups. Here, we construct $(2, 3)$-generators for the finite odd-dimensional orthogonal groups…

Using only undergraduate-level methods, we classify all groups of order $p^4$, where $p$ is an odd prime.

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

We consider the quotient group $T(G)$ of the multiple holomorph by the holomorph of a finite $p$-group $G$ of class two for an odd prime $p$. By work of the first-named author, we know that $T(G)$ contains a cyclic subgroup of order…

Let $p$ be a prime number and $\mathbb{Z}_p=\mathbb{Z}/p\mathbb{Z}$. We study finite groups with abelian derived subgroup and exponent $p$ in terms of group extension data and their matrix presentations. We show a one-to-one correspondence…

The coexponent of a finite p-group is introduced and we consider how the nilpotency class is bounded in terms of this invariant.

In this paper, we investigate the edge-coloring number of the power graph of a finite group. We characterize which finite groups have overfull power graphs, showing that this occurs if and only if the group is cyclic of odd prime power…

A new general formula for the number of conjugacy classes of subgroups of given index in a finitely generated group is obtained.

There is a probability charge on the power set of the integers that gives probability $1/p$ to every residue class modulo a prime $p$. There exists such a charge that gives probability $w$ to the set of prime numbers iff $w \in [0,1/2]$.…

Let G be a 2-group of order 2^n, n>5, and nilpotency class n-2. The invariants of such groups determined by their group algebras over the field of two elements are given in the paper.

We establish new examples and non-examples of pro-p limit groups among the class of Demushkin groups, that is, pro-p Poincar\'e duality groups of dimension 2.

This paper concerns finite groups of class (at most) two and of odd prime exponent $p$. Such a group is called special if the center lies within its derived group. Every group of class 2 and exponent $p$ can be uniquely expressed as the…