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Displaying 201 – 220 of 278

The Artin exponent of finite groups

Kenneth K. Nwabueze (1997)

Acta Mathematica et Informatica Universitatis Ostraviensis

The automorphism group of a p-group of maximal class with an abelian maximal subgroup

Alphonse Baartmans, James Woeppel (1976)

Fundamenta Mathematicae

The Bogomolov multiplier of groups of order $p^{7}$ and exponent $p$

Zeinab Araghi Rostami, Mohsen Parvizi, Peyman Niroomand (2024)

Czechoslovak Mathematical Journal

We conduct an in-depth investigation into the structure of the Bogomolov multiplier for groups of order $p^{7}$ $(p > 2)$ and exponent $p$ . We present a comprehensive...

The classification of finite groups by using iteration digraphs

Uzma Ahmad, Muqadas Moeen (2016)

Czechoslovak Mathematical Journal

A digraph is associated with a finite group by utilizing the power map $f : G \to G$ defined by $f (x) = x^{k}$ for all $x \in G$ , where $k$ is a fixed natural number. It is denoted by $γ_{G} (n, k)$ . In this paper, the generalized quaternion and $2$ -groups are studied. The height structure is discussed for the generalized quaternion. The necessary and sufficient conditions on a power digraph of a $2$ -group are determined for a $2$ -group to be a generalized quaternion group. Further, the classification of two generated $2$ -groups as abelian or non-abelian...

The conjugacy vector of a p-group of maximal class (I)

Antonio Vera López, Gustavo A. Fernández Alcober (1989)

Extracta Mathematicae

The distribution of second $p$ -class groups on coclass graphs

Daniel C. Mayer (2013)

Journal de Théorie des Nombres de Bordeaux

General concepts and strategies are developed for identifying the isomorphism type of the second $p$ -class group $G = Gal (F_{p}^{2} (K) | K)$ , that is the Galois group of the second Hilbert $p$ -class field $F_{p}^{2} (K)$ , of a number field $K$ , for a prime $p$ . The isomorphism type determines the position of $G$ on one of the coclass graphs $𝒢 (p, r)$ , $r \geq 0$ , in the sense of Eick, Leedham-Green, and Newman. It is shown that, for special types of the base field $K$ and of its $p$ -class group ${Cl}_{p} (K)$ , the position of $G$ is restricted to certain admissible branches of coclass...

The function g(h) for which |A(G)|p>=p^h whenever |G|>=p^g(h) , G a finite P-group

M. V. D. Burmester, Th. G. Exarhakos (1988)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

The Hughes subgroup

Robert Bryce (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $G$ be a group and $p$ a prime. The subgroup generated by the elements of order different from $p$ is called the Hughes subgroup for exponent $p$ . Hughes [3] made the following conjecture: if $H_{p} (G)$ is non-trivial, its index in $G$ is at most $p$ . There are many articles that treat this problem. In the present Note we examine those of Strauss and Szekeres [9], which treats the case $p = 3$ and $G$ arbitrary, and that of Hogan and Kappe [2] concerning the case when $G$ is metabelian, and $p$ arbitrary. A common proof is...

The number of conjugacy classes in a finite nilpotent group

Antonio Vera Lopez (1985)

Rendiconti del Seminario Matematico della Università di Padova

The pi-separability of Certain Factorizable Groups.

Peter J. Rowley (1977)

Mathematische Zeitschrift

The Roquette category of finite $p$ -groups

Serge Bouc (2015)

Journal of the European Mathematical Society

Let $p$ be a prime number. This paper introduces the Roquette category $ℛ_{p}$ of finite $p$ -groups, which is an additive tensor category containing all finite $p$ -groups among its objects. In $ℛ_{p}$ , every finite $p$ -group $P$ admits a canonical direct summand $\partial P$ , called the edge of $P$ . Moreover $P$ splits uniquely as a direct sum of edges of Roquette $p$ -groups, and the tensor structure of $ℛ_{p}$ can be described in terms of such edges. The main motivation for considering this category is that the additive functors from $ℛ_{p}$ to...

The structure of finite p-groups: effective proof of the coclass conjectures.

Aner Shalev (1994)

Inventiones mathematicae

Theta pairs and the structure of finite groups.

Li, Xianhua, Li, Shiheng (2004)

Sibirskij Matematicheskij Zhurnal

Über die Untergruppen der elementarabelschen Gruppen

L. TESCHKE (1975)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Über direkte Produkte von k-regulären p-Gruppen

Wolfgang Bannuscher (1984)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Über minimale k-irreguläre p-Gruppen I

Wolfgang Bannuscher (1987)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Über minimale k-irreguläre p-Gruppen II

W. BANNUSCHER (1987)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Über ...-Ringstrukturen auf dem Burnside-Ring.

Tammo tom Dieck (1984)

Mathematische Zeitschrift

Un problema sul gruppo degli automorfismi di un $p$ -gruppo finito

Federico Menegazzo (1983)

Rendiconti del Seminario Matematico della Università di Padova

Un'osservazione sulle classi di Fitting normali

Guido Zappa (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We prove that a Fitting class of finite soluble groups is normal if and only if it verifies the condition $\alpha$ ) (see n. 2). Unlike the definition of normal Fitting class, this condition is “constructive”.

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