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Browsing by Subject "Conjugacy classes"

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Browsing by Subject "Conjugacy classes"

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    An Arad and Fisman's theorem on products of conjugacy classes revisited 
    Beltrán Felip, Antonio; Felipe Román, María José; Melchor, Carmen (Springer-Verlag, 2022-12)
    [EN] A theorem of Z. Arad and E. Fisman establishes that if A and B are two non-trivial conjugacy classes of a finite group G such that either AB = A boolean OR B or AB = A(-1) boolean OR B, then G cannot be a non-abelian ...
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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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    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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    Conjugacy classes contained in normal subgroups: an overview 
    Beltrán, Antonio; Felipe, María José; Melchor, Carmen (University of Isfahan, 2018)
    [EN] We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework ...
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    Cosets of normal subgroups and powers of conjugacy classes 
    Beltrán, Antonio; Felipe Román, María Josefa (John Wiley & Sons, 2021-09)
    [EN] Let G be a finite group and let K=xG be the conjugacy class of an element x of G. In this paper, it is proved that if N is a normal subgroup of G such that the coset xN is the union of K and K-1 (the conjugacy class ...
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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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    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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    Local convergence and dynamical analysis of a new family of optimal fourth-order iterative methods 
    Artidiello Moreno, Santiago de Jesús; Chicharro López, Francisco Israel; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón (Taylor & Francis Ltd, 2013-10)
    In this paper, a family of new fourth-order optimal iterative methods for solving nonlinear equations is proposed. The classical King s family of fourth-order schemes is obtained as an special case. We also present results ...
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    On finite groups with square-free conjugacy class sizes 
    Felipe, María José; Martínez Pastor, Ana; Sotomayor, Víctor (University of Isfahan, 2018)
    [EN] We report on fi nite groups having square-free conjugacy class sizes, in particular in the framework of factorised groups.
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    On products of groups and indices not divisible by a given prime 
    Felipe Román, María Josefa; Kazarin, Lev S.; Martínez-Pastor, Ana; Sotomayor, Víctor (Springer-Verlag, 2020-12)
    [EN] Let the group G = AB be the product of subgroupsAandB, and letpbe a prime. We prove thatpdoes not divide the conjugacy class size (index) of eachp-regular element of prime power order x is an element of A boolean OR ...
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    On zeros of irreducible characters lying in a normal subgroup 
    Felipe Román, María Josefa; Grittini, N.; Sotomayor, Víctor (Springer-Verlag, 2020-10)
    [EN] Let N be a normal subgroup of a finite group G. In this paper, we consider the elements g of N such that x(g)¿0 for all irreducible characters x of G. Such an element is said to be non-vanishing in G. Let p be a prime. ...
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    Powers of conjugacy classes in a finite groups 
    Beltrán, Antonio; Camina, Rachel Deborah; Felipe Román, María Josefa; Melchor, Carmen (Springer-Verlag, 2020-04)
    [EN] The aim of this paper is to show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper was to show several results about solvability ...
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    Prime power indices in factorised groups 
    Felipe Román, María Josefa; Martínez-Pastor, Ana; Sotomayor, Víctor (Springer-Verlag, 2017)
    [EN] Let the group G = AB be the product of the subgroups A and B. We determine some structural properties of G when the p-elements in A. B have prime power indices in G, for some prime p. More generally, we also consider ...
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    Products of groups and class sizes of pi-elements 
    Felipe Román, María José; Martínez-Pastor, Ana; Sotomayor, Víctor (Springer-Verlag, 2020-02)
    [EN] We provide structural criteria for some finite factorised groups G = AB when the conjugacy class sizes in G of certain pi-elements in A boolean OR B are either pi-numbers or pi'-numbers, for a set of primes pi. In ...
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    Some problems about products of conjugacy classes in finite groups 
    Beltran, Antonio; Felipe Román, María Josefa; Melchor, Carmen (University of Isfahan, 2020-03)
    [EN] We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect ...
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    Square-free class sizes in products of groups 
    Felipe, María José; Martínez Pastor, Ana; Sotomayor, Víctor (Elsevier, 2017)
    [EN] We obtain some structural properties of a factorised group G = AB, given that the conjugacy class sizes of certain elements in A boolean OR B are not divisible by p(2), for some prime p. The case when G = AB is a ...
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    Squares of real conjugacy classes in finite groups 
    Beltrán, A.; Felipe Román, María Josefa; Melchor, C. (Springer-Verlag, 2018)
    [EN] We prove that if a finite group G contains a conjugacy class K whose square is of the form 1¿D, where D is a conjugacy class of G, then ¿K¿ is a solvable proper normal subgroup of G and we completely determine its ...
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    Triangles in the graph of conjugacy classes of normal subgroups 
    Beltrán, Antonio; Felipe Román, María Josefa; Melchor, Carmen (Springer-Verlag, 2017-01)
    [EN] Let G be a finite group and N a normal subgroup of G. We determine the structure of N when the graph G(N), which is the graph associated to the conjugacy classes of G contained in N, has no triangles and when the graph ...
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    Zeros of irreducible characters in factorised groups 
    Sotomayor, Víctor; Felipe Román, María Josefa; Martínez-Pastor, Ana (Springer-Verlag, 2019-02)
    [EN] An element g of a finite group G is said to be vanishing inG if there exists an irreducible character of G such that (g)=0; in this case, g is also called a zero of G. The aim of this paper is to obtain structural ...