Erratum to: “Solitary quotients of finite groups”
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”
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.
Every -group with all subgroups normal-by-finite is locally finite
A group has all of its subgroups normal-by-finite if is finite for all subgroups of . The Tarski-groups provide examples of -groups ( 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 -group with every subgroup normal-by-finite is locally finite. We also prove that if for every subgroup of , then contains an Abelian subgroup of index at most .
Exact covering systems for groups
Examples of complete groups of odd order
Exceptional groups of Lie type as Galois groups.
Existencia de inyectores en grupos finitos respecto de ciertas clases de Fitting.
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
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].
Exponents of almost simple groups and an application to the restricted Burnside problem.
Exponents of modules and maps.
Extended near hexagons and line systems.
Extreme elements of finite -groups
Factoring Abelian groups of order .
Factoring an odd abelian group by lacunary cyclic subsets
It is a known result that if a finite abelian group of odd order is a direct product of lacunary cyclic subsets, then at least one of the factors must be a subgroup. The paper gives an elementary proof that does not rely on characters.
Factoring by nonsubgroup factors.
Factorization of groups involving symmetric and alternating groups.
Factorization problems in class number two
Factorization results with combinatorial proofs.
Factorizations and Paige's theorem on complete maps.