Listar por autoría "015e6ea7-b5de-4423-a01e-f35467458c6f"
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A coprime action version of a solubility criterion of Deskins
Springer Verlag (2019)Let A and G be finite groups of relatively prime orders and suppose that A acts on G via automorphisms. We demonstrate that if G has a maximal A-invariant subgroup M that is nilpotent and the Sylow 2-subgroup of M has ... -
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 ...
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An Arad and Fisman’s Theorem on Products of Conjugacy Classes Revisited
Springer (2022)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 ∪ B or AB = A−1 ∪ B, then G cannot be a non-abelian simple group. We ...
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Arithmetical Conditions on Invariant Sylow Numbers
Springer Verlag (2018)Let A and G be finite groups and suppose that A acts coprimely on G via automorphisms. A natural number n is said to be an A-invariant Sylow number if n is the number of A-invariant Sylow p-subgroups of G for some prime ... -
c-Normality and coprime action in finite groups
Springer (2023-10-31)A subgroup H of a finite group G is called c-normal if there exists a normal subgroup N in G such that G = HN and , the largest normal subgroup of G contained in H. c-Normality is a weaker form of normality, introduced by ...
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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 ...
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Conditions for Sylow 2-subgroups of the Fixed Point Subgroup Implying Solubility
Cambridge University Press (2018)Let A and G be finite groups and suppose that A acts via automorphisms on G with (|A|, |G|) = 1. We study how certain conditions on the Sylow 2-subgroups of the fixed point subgroup of the action, CG(A), may imply the ...
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Conjugacy classes and union of cosets of normal subgroups
Springer Nature (2023)Let G be a finite group, N a normal subgroup of G and K a conjugacy class of G. We prove that if K∪K−1 is union of cosets of N, then N is soluble, K is a real-imaginary class, that is, every irreducible character of G takes ...
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Conjugacy classes and union of cosets of normal subgroups
Springer (2023)Let G be a finite group, N a normal subgroup of G and K a conjugacy class of G. We prove that if K ∪ K −1 is union of cosets of N, then N is soluble, K is a real-imaginary class, that is, every irreducible character of ...
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Conjugacy classes contained in normal subgroups: an overview
University of Isfahan (2017)We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an in uence on the normal structure of a nite group. The approach is mainly presented in the framework ...
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Coprime action and arithmetical conditions on invariant conjugacy classes
Springer Verlag (2015-12)Let A and G be finite groups and suppose that A acts coprimely on G via automorphisms. We show that if 4 divides no A-invariant conjugacy class size of G, then G is solvable. We also characterize the A-invariant structure ...
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Corrigendum to "Variations on a theorem by Alan Camina on conjugacy class sizes" [J. Algebra 296 (2006) 253-266]
Elsevier (2008)[No abstract available]
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Corrigendum to: “A coprime action version of a solubility criterion of Deskins”
Springer Verlag (2020-01-14)In this Corrigendum we correct a missed case in the statement of Theorem 2.4 and a subsequent mistake in the proof of the main result in “A coprime action version of a solubility criterion of Deskins”, Monatsh. Math. ...
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Cosets of normal subgroups and powers of conjugacy classes
Wiley (2021-08-03)Let 𝐺 be a finite group and let𝐾 = 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 ...
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Existence of normal Hall subgroups by means of orders of products
Wiley-VCH Verlag (2018)Let G be a finite group, let π be a set of primes and let p be a prime. We characterize the existence of a normal Hall π‐subgroup in G in terms of the order of products of certain elements of G. This theorem generalizes a ...
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Extending Camina pairs
Elsevier (2023)Let G be a finite group and N a nontrivial proper normal subgroup of G. A.R. Camina introduced the class of finite groups G, which extends Frobenius groups, satisfying that for all g ∈ G − N and n ∈ N, gn is conjugate ...
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Finite Groups with Four Conjugacy Class Sizes
Taylor & Francis (2012-10-01)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}, where ...
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Finite groups with two p-regular conjugacy class lengths II
Australian Mathematical Publishing Association (2009)Let G be a finite group. We prove that if the set of p-regular conjugacy class sizes of G has exactly two elements, then G has Abelian p-complement or G=PQ×A, with P∈Sylp(G), Q∈Sylq(G) and A Abelian.
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Finite p-solvable groups with three p-regular conjugacy class sizes
Edinburgh Mathematical Society (2013)Let G be a finite p-solvable group. We describe the structure of the p-complements of G when the set of p-regular conjugacy classes has exactly three class sizes. For instance, when the set of p-regular class sizes of G ...
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Indices of Maximal Invariant Subgroups and Solvability of Finite Groups
Springer Verlag (2019)Let A and G be finite groups and suppose that A acts coprimely on G via automorphisms. We study the solvability and supersolvability of G when certain proper maximal A-invariant subgroups of G have prime index or when ...
