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Displaying 521 – 540 of 1356

On a generalization of a theorem of Burnside

Jiangtao Shi (2015)

Czechoslovak Mathematical Journal

A theorem of Burnside asserts that a finite group $G$ is $p$ -nilpotent if for some prime $p$ a Sylow $p$ -subgroup of $G$ lies in the center of its normalizer. In this paper, let $G$ be a finite group and $p$ the smallest prime divisor of $| G |$ , the order of $G$ . Let $P \in {Syl}_{p} (G)$ . As a generalization of Burnside’s theorem, it is shown that if every non-cyclic $p$ -subgroup of $G$ is self-normalizing or normal in $G$ then $G$ is solvable. In particular, if $P ≇ 〈 a, b | a^{p^{n - 1}} = 1, b^{2} = 1, b^{- 1} a b = a^{1 + p^{n - 2}} 〉$ , where $n \geq 3$ for $p > 2$ and $n \geq 4$ for $p = 2$ , then $G$ is $p$ -nilpotent or $p$ -closed.

On a generalization of Fermat's theorem in the theory of groups

A. Krapež (1974)

Publications de l'Institut Mathématique

On a generalization of Fermat's theorem in the theory of groups.

A. Krapez (1974)

Publications de l'Institut Mathématique [Elektronische Ressource]

On a group acting locally freely on an Abelian group.

Zhurtov, A. Kh. (2003)

Sibirskij Matematicheskij Zhurnal

On a group that acts freely on an Abelian group.

Mazurov, V.D., Churkin, V.A. (2001)

Sibirskij Matematicheskij Zhurnal

On a group-theoretical generalization of the Gauss formula

Georgiana Fasolă, Marius Tărnăuceanu (2023)

Czechoslovak Mathematical Journal

We discuss a group-theoretical generalization of the well-known Gauss formula involving the function that counts the number of automorphisms of a finite group. This gives several characterizations of finite cyclic groups.

On a problem of A.D. Sands.

Sándor Szabó (1989)

Aequationes mathematicae

On a problem of the theory of multiply local formations.

Guo, Wenbin (2004)

Sibirskij Matematicheskij Zhurnal

On a question of Chambers and Makan.

A. Ballester-Bolinches, M. Pérez-Ramos (1996)

Mathematische Zeitschrift

On a Theorem of Burnside.

R.W. van der Waall (1970)

Elemente der Mathematik

On a theorem of Frobenius.

Bakić, Radoš (1997)

Publications de l'Institut Mathématique. Nouvelle Série

On a theorem of Frobenius.

Käte Fenchel (1978)

Mathematica Scandinavica

On a Theorem of Thompson Concerning a Class of Non-Solvable Groups.

John Randolph (1970)

Mathematische Zeitschrift

On a variation of Sands' method.

Obaid, Evelyn E. (1986)

International Journal of Mathematics and Mathematical Sciences

On abelian inner mapping groups of finite loops

Markku Niemenmaa (2000)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider finite loops of specific order and we show that certain abelian groups are not isomorphic to inner mapping groups of these loops. By using our results we are able to construct a finite solvable group of order 120 which is not isomorphic to the multiplication group of a finite loop.

On Alperin's fusion theorem.

Stellmacher, Bernd (1994)

Beiträge zur Algebra und Geometrie

On automorphism groups of finite $p$ -groups

Izabela Malinowska (1994)

Rendiconti del Seminario Matematico della Università di Padova

On Bialostocki's conjecture for zero-sum sequences

Song Guo, Zhi-Wei Sun (2009)

Acta Arithmetica

On B-injectors of symmetric groups Sₙ and alternating groups Aₙ: a new approach

M. I. AlAli, Bilal Al-Hasanat, I. Sarayreh, M. Kasassbeh, M. Shatnawi, A. Neumann (2009)

Colloquium Mathematicae

The aim of this paper is to introduce the notion of BG-injectors of finite groups and invoke this notion to determine the B-injectors of Sₙ and Aₙ and to prove that they are conjugate. This paper provides a new, more straightforward and constructive proof of a result of Bialostocki which determines the B-injectors of the symmetric and alternating groups.

On Camina group and its generalizations

A. S. Muktibodh, S. H. Ghate (2013)

Matematički Vesnik

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