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Equivalent conditions for p-nilpotence

Keresztély Corrádi, Erzsébet Horváth (2000)

Discussiones Mathematicae - General Algebra and Applications

In the first part of this paper we prove without using the transfer or characters the equivalence of some conditions, each of which would imply p-nilpotence of a finite group G. The implication of p-nilpotence also can be deduced without the transfer or characters if the group is p-constrained. For p-constrained groups we also prove an equivalent condition so that $O^{q^{'}} (G) P$ should be p-nilpotent. We show an example that this result is not true for some non-p-constrained groups. In the second part of the...

Errata-Corrige : “Some sporadic groups as Galois groups II”

H. Pahlings (1991)

Rendiconti del Seminario Matematico della Università di Padova

Erratum to 'Rational Lie Algebras and p-Isomorphisms of Nilpotent Groups and Homotopy Types'

Joseph Roitberg (1976)

Commentarii mathematici Helvetici

Erratum to: “Solitary quotients of finite groups”

Marius Tărnăuceanu (2013)

Open Mathematics

In this short note a correct proof of Theorem 3.3 from [Tărnăuceanu M., Solitary quotients of finite groups, Cent. Eur. J. Math., 2012, 10(2), 740–747] is given.

Erratum to: “Subnormal, permutable, and embedded subgroups in finite groups”

James Beidleman, Mathew Ragland (2012)

Open Mathematics

The original version of the article was published in Central European Journal of Mathematics, 2011, 9(4), 915–921, DOI: 10.2478/s11533-011-0029-8. Unfortunately, the original version of this article contains a mistake: Lemma 2.1 (2) is not true. We correct Lemma 2.2 (2) and Theorem 1.1 in our paper where this lemma was used.

Estimation of the order of a group generated by a twisted subset.

Belyaev, V.V., Myl'nikov, A.L. (2008)

Sibirskij Matematicheskij Zhurnal

Every $2$ -group with all subgroups normal-by-finite is locally finite

Enrico Jabara (2018)

Czechoslovak Mathematical Journal

A group $G$ has all of its subgroups normal-by-finite if $H / H_{G}$ is finite for all subgroups $H$ of $G$ . The Tarski-groups provide examples of $p$ -groups ( $p$ a “large” prime) of nonlocally finite groups in which every subgroup is normal-by-finite. The aim of this paper is to prove that a $2$ -group with every subgroup normal-by-finite is locally finite. We also prove that if $| H / H_{G} | \leq 2$ for every subgroup $H$ of $G$ , then $G$ contains an Abelian subgroup of index at most $8$ .

Exact covering systems for groups

M. Parmenter (1984)

Fundamenta Mathematicae

Examples of complete groups of odd order

Hermann Heineken (1996)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Exceptional groups of Lie type as Galois groups.

Gunter Malle (1988)

Journal für die reine und angewandte Mathematik

Existencia de inyectores en grupos finitos respecto de ciertas clases de Fitting.

María Jesús Iranzo, Francisco Pérez Monasor (1988)

Publicacions Matemàtiques

In this paper we prove that all finite groups have F-injectors with respect to a saturated and extensible Fitting formation F.

Expansion in finite simple groups of Lie type

Emmanuel Breuillard, Ben J. Green, Robert Guralnick, Terence Tao (2015)

Journal of the European Mathematical Society

We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the Bourgain-Gamburd method and on the main result of our companion paper [BGGT].

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