Kazarin, L. S.; Martínez Pastor, Ana; Perez Ramos, Maria Dolores(Elsevier, 2013-04-01)
[EN] For a set of primes pi, a group X is said to be pi-decomposable if X = X-pi x X-pi' is the direct product of a pi-subgroup X-pi and a pi'-subgroup X-pi', where pi' is the complementary of pi in the set of all prime ...
[EN] The purpose of this work is to analyze results on the overall structure of a factorised group from certain information about the sizes of the conjugacy classes of some elements of its factors.
Beltrán, Antonio; Felipe Román, María Josefa; Shao, Changguo(Springer Verlag (Germany), 2015-10)
We prove an extension of the renowned Itô’s theorem on groups having two class sizes in three different directions at the same time: normal subgroups, p′p′-elements and prime-power order elements. Let NN be a normal subgroup ...
[ES] Un problema clásico en la teoría de grupos finitos es el estudio de cómo los tamaños de las clases de conjugación influyen sobre la estructura del grupo. En las últimas décadas, numerosos investigadores han obtenido ...
Beltrán, Antonio; Felipe Román, María Josefa; SHAO, CHANG GUO(World Scientific Publishing, 2012-12)
The authors have realized that in the proof of Theorem 6 of [1] there is a mistake
although the conclusion of the theorem is correct. The proof of the theorem is
divided into two cases: when there exist no p-elements of ...
Beltrán, Antonio; Felipe Román, María Josefa(Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2011-03-18)
We determine the structure of all finite groups with four class sizes when two of them are coprime numbers larger than 1. We prove that such groups are solvable and that the set of class sizes is exactly {1, m, n, mk}, ...
Ballester-Bolinches, A.; Cossey, John; Esteban Romero, Ramón(Universita del Salento, 2013)
[EN] There are different ways to associate to a finite group a certain graph. An interesting question is to analyse the relations between the structure of the group, given in group-theoretical terms, and the structure of ...
Beltrán, Antonio; Felipe Román, María Josefa; Melchor, Carmen(Elsevier, 2015-12-01)
Let G be a finite group and let N be a normal subgroup of G.
We attach to N two graphs ΓG(N) and Γ∗
G(N) related to the
conjugacy classes of G contained in N and to the set of primes
dividing the sizes of these classes, ...
Alemany Martínez, Elena; Beltrán, Antonio; Felipe Román, María Josefa(Cambridge University Press, 2012)
Let G be a finite p-solvable group. We prove that if G has exactly two conjugacy class sizes of p'-elements of prime power order, say 1 and m, then m = p(a)q(b), for two distinct primes p and q, and G either has an abelian ...
Beltran, Antonio; Felipe Román, María José; Melchor, Carmen(World Scientific Publishing, 2016-11)
Landau's theorem on conjugacy classes asserts that there are only finitely many finite groups, up to isomorphism, with exactly k conjugacy classes for any positive integer k. We show that, for any positive integers n and ...
A subgroup H of a group G is said r to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite ...
Akhlaghi, Zeinab; Beltrán Felip, Antonio; Felipe Román, María Josefa(Elsevier, 2014-02-01)
If G is a finite group, we show that any normal subgroup of G
which has exactly three G-conjugacy class sizes is solvable. Thus,
we give an extension for normal subgroups of the classical N. Itô’s
theorem which asserts ...
Akhlaghi, Zeinab; Beltrán Felip, Antonio; Felipe Román, María Josefa; Khatami, Maryam(Elsevier, 2011-06-15)
Let G be a finite p-solvable group and N be a normal subgroup of G. Suppose that the p-regular elements of N have exactly two G-conjugacy class sizes. In this paper it is shown that, if H is a p-complement of N, then either ...
Ballester Bolinches, Adolfo; Esteban Romero, Ramón; Jiang, Qinhui; Li, Xianhua(SpringerFondazione Annali di Matematica Pura ed Applicata, 2015-02)
In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An A 5 -free group possessing one of these families is soluble, and soluble groups with this property have ...
Two subgroups and of a group are said to be totally completely conditionally permutable (tcc-permutable) if permutes with for some , for all and all . In this paper, we study finite products of tcc-permutable subgroups, ...
Two subgroups A and B of a group G are said to be totally completely conditionally permutable (tcc-permutable) in G if X permutes with Yg for some g ¿ ¿X, Y¿ for all X ¿ A and Y ¿ B. We study the belonging of a finite ...
Two subgroups X and Y of a group G are said to be conditionally permutable in G if X permutes with Y(g) for some element g E G. i.e., XY(g) is a subgroup of G. Using this permutability property new criteria for the product ...