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Browsing by Subject "Finite groups"

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Browsing by Subject "Finite groups"

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    A reduction theorem for a conjecture on products of two ¿-decomposable groups 
    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 ...
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    A Survey on Sylow Normalizers and Classes of Groups 
    D'Aniello, A.; Kazarin, L.S.; Martínez Pastor, Ana; Perez Ramos, Maria Dolores (HIKARI Ltd, 2014)
    We report on a stream of research in relation with Sylow normalizers, i.e. normalizers of Sylow subgroups, of finite groups and group’s classes.
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    Clases de conjugación y grupos factorizados 
    Ortiz Sotomayor, Víctor Manuel (Universitat Politècnica de València, 2016-07-20)
    [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.
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    Class sizes of prime-power order p'-elements and normal subgroups 
    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 ...
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    Conditional permutability of subgroups and certain classes of groups 
    Arroyo Jordá, Milagros; Arroyo Jordá, Paz (Elsevier, 2017)
    [EN] Two subgroups A and B of a finite group G are said to be tcc-permutable if X permutes with Y for some g epsilon (X, Y), for all X <= A and all Y <= B. Some aspects about the normal structure of a product of two ...
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    Conjugacy classes and factorised groups 
    Ortiz Sotomayor, Víctor Manuel (Universitat Politècnica de València, 2019-09-02)
    [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 ...
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    Corrigendum on the solvability of groups with four class sizes 
    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 ...
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    Finite groups whose prime graph on class sizes is a block square 
    Sotomayor, Víctor (Taylor & Francis, 2022-09-02)
    [EN] Let G be a finite group, and let Delta(G) be the prime graph built on its set of conjugacy class sizes: this is the (simple undirected) graph whose vertices are the prime numbers dividing some conjugacy class size of ...
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    Finite groups with four conjugacy class sizes 
    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}, ...
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    Finite trifactorized groups and pi-decomposability 
    Kazarin, L. S.; Martínez-Pastor, Ana; Perez Ramos, Maria Dolores (Cambridge University Press, 2018)
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    Graphs and classes of finite groups 
    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 ...
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    Graphs associated to conjugacy classes of normal subgroups in finite groups 
    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, ...
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    Itô's theorem on groups with two class sizes revisited 
    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 ...
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    Landau's theorem on conjugacy classes for normal subgroups 
    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 ...
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    Maximal subgroups and PST-groups 
    Ballester-Bolinches, A.; Beidleman, J.C.; Esteban Romero, Ramón; Pérez-Calabuig, V. (Springer Verlag (Germany), 2013-06)
    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 ...
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    Normal sections, class sizes and solvability of finite groups 
    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 ...
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    Normal subgroups and p-regular G-class sizes 
    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 ...
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    On a class of generalised Schmidt groups 
    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 ...
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    On conditional permutability and factorized groups 
    Arroyo Jordá, Milagros; Arroyo Jordá, Paz; Martínez Pastor, Ana; Perez Ramos, Maria Dolores (Springer Verlag (Germany), 2014-08)
    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, ...
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    On conditional permutability and saturated formations 
    Arroyo Jordá, Milagros; Arroyo Jordá, Paz; M.D. Pérez-Ramos (Cambridge University Press, 2011)
    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 ...