ListarDepartament: Matemàtiques por tema "Normal subgroups"
Mostrando ítems 1-6 de 6
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A criterion for a normal subgroup to be hypercentral based on class sizes
Springer (2024)Let G be a finite group and N a normal subgroup of G. We prove that the knowledge of the sizes of the conjugacy classes of G that are contained in N and of their multiplicities provides information of N in relation to the ... -
Class sizes of prime-power orden p'-elements and normal subgroups
Springer (2014-06)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' -elements and prime- power order elements. Let N be a normal subgroup ... -
Landau's theorem on conjugacy classes for normal subgroups
World Scientific (2016-10-10)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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Simplicity of normal subgroups and conjugacy class sizes
Springer (2013)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 ...
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Structure of normal subgroups with three G-class sizes
Springer-Verlag (2012)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
Springer (2015-12)Let G be a finite group and N a normal subgroup of G. We determine the structure of N when the graph ΓG(N), which is the graph associated to the conjugacy classes of G contained in N, has no triangles and when the graph ...
