Displaying similar documents to “A remark on a Theorem of J. G. Thompson”

The Hughes subgroup

Robert Bryce (1994)

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

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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...

Injectors of fitting classes of 𝔊 1 -groups

Federico Menegazzo, Martin L. Newell (1988)

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

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Fitting classes and injectors are discussed in the class of 𝔊 1 -groups. A necessary and sufficient condition for the existence of injectors is given; it is also shown that, when this condition holds, the injectors form a unique conjugacy class.

A characterization of the linear groups L 2 ( p )

Alireza Khalili Asboei, Ali Iranmanesh (2014)

Czechoslovak Mathematical Journal

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Let G be a finite group and π e ( G ) be the set of element orders of G . Let k π e ( G ) and m k be the number of elements of order k in G . Set nse ( G ) : = { m k : k π e ( G ) } . In fact nse ( G ) is the set of sizes of elements with the same order in G . In this paper, by nse ( G ) and order, we give a new characterization of finite projective special linear groups L 2 ( p ) over a field with p elements, where p is prime. We prove the following theorem: If G is a group such that | G | = | L 2 ( p ) | and nse ( G ) consists of 1 , p 2 - 1 , p ( p + ϵ ) / 2 and some numbers divisible by 2 p , where p is a prime...

Notes on the average number of Sylow subgroups of finite groups

Jiakuan Lu, Wei Meng, Alexander Moretó, Kaisun Wu (2021)

Czechoslovak Mathematical Journal

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We show that if the average number of (nonnormal) Sylow subgroups of a finite group is less than 29 4 then G is solvable or G / F ( G ) A 5 . This generalizes an earlier result by the third author.

Injectors of fitting classes of 𝔊 1 -groups

Federico Menegazzo, Martin L. Newell (1988)

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

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Fitting classes and injectors are discussed in the class of 𝔊 1 -groups. A necessary and sufficient condition for the existence of injectors is given; it is also shown that, when this condition holds, the injectors form a unique conjugacy class.

On absolutely-nilpotent of class k groups

Patrizia Longobardi, Trueman MacHenry, Mercede Maj, James Wiegold (1995)

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

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A group G in a variety V is said to be absolutely- V , and we write G A V , if central extensions by G are again in V . Absolutely-abelian groups have been classified by F. R. Beyl. In this paper we concentrate upon the class A N k of absolutely-nilpotent of class k groups. We prove some closure properties of the class A N k and we show that every nilpotent of class k group can be embedded in an A N k -gvoup. We describe all metacyclic A N k -groups and we characterize 2 -generator and infinite 3 -generator A N 2 -groups....

The superfocal subgroup

Marian Deaconescu (1984)

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

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Nel presente lavoro vengono dimostrati teoremi d'esistenza di p -complementi normali nei gruppi finiti.

On TI-subgroups and QTI-subgroups of finite groups

Ruifang Chen, Xianhe Zhao (2020)

Czechoslovak Mathematical Journal

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Let G be a group. A subgroup H of G is called a TI-subgroup if H H g = 1 or H for every g G and H is called a QTI-subgroup if C G ( x ) N G ( H ) for any 1 x H . In this paper, a finite group in which every nonabelian maximal is a TI-subgroup (QTI-subgroup) is characterized.

Symmetry classes of tensors associated with the semi-dihedral groups S D 8 n

Mahdi Hormozi, Kijti Rodtes (2013)

Colloquium Mathematicae

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We discuss the existence of an orthogonal basis consisting of decomposable vectors for all symmetry classes of tensors associated with semi-dihedral groups S D 8 n . In particular, a necessary and sufficient condition for the existence of such a basis associated with S D 8 n and degree two characters is given.