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Listar por palabra clave "Normal subgroups"

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Listar por palabra clave "Normal subgroups"

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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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    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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    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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    On the group of homeomorphisms on R: A revisit 
    Ali Akbar, Kamaludheen; Mubeena, T. (Universitat Politècnica de València, 2022-10-03)
    [EN]  In this article, we prove that the group of all increasing homeomorphisms on R has exactly five normal subgroups, and the group of all homeomorphisms on R has exactly four normal subgroups. There are several results ...
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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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    p-divisibility of conjugacy class sizes and normal p-complements 
    Beltrán, Antonio; Felipe Román, María Josefa; Shao, Changguo (De Gruyter, 2015-01)
    . Let N be a normal subgroup of a group G and let p be a prime. We prove that if the p-part of jx Gj is a constant for every prime-power order element x 2 N n Z.N /, then N is solvable and has normal p-complement.
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    Simplicity of normal subgroups and conjugacy class sizes 
    Beltrán, Antonio; Felipe Román, María Josefa (Springer Verlag (Germany), 2014-12)
    Given a finite group G which possesses a non-abelian simple normal subgroup N having exactly four G-class sizes, we prove that N is isomorphic to PSL(2,2a) with a≥2. Thus, we obtain an extension for normal subgroups of the ...
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    Structure of normal subgroups with three G-class sizes 
    Akhlaghi, Z.; Beltrán, Antonio; Felipe Román, María Josefa; Khatami, M. (Springer Verlag (Germany), 2012-07)
    Let G be a finite group and N be a normal subgroup of G. Suppose that the set of G-conjugacy class sizes of N is {1, m, n}, with m < n and m does not divide n. In this paper, we show that N is solvable, and we determine ...
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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 ...