Listar por autoría "9d526318-7810-4a53-bba2-32e83e72a4e1"
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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 ... -
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 ... -
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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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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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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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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ItÔ's Theorem on Groups with two class sizes revisited
Australian Mathematical Publishing Association (2012-06)LetG be a finite p-solvable group. We prove that ifG has exactly two conjugacy class sizes of p 0 -elements of prime power order, say 1 and m, then m = p aq b , for two distinct primes p and q, and G either has ...
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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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Multiplying a conjugacy class by its inverse in a finite group
Springer (2018-08)Suppose that G is a finite group and K is a non-trivial conjugacy class of G such that KK−1 = 1 ∪ D ∪ D−1 with D a conjugacy class of G. We prove that G is not a non-abelian simple group and we give arithmetical conditions ...
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Nilpotency of normal subgroups having two G-class sizes
American Mathematical Society (2010-12-22)Let G be a finite group. If N is a normal subgroup which has exactly two G-conjugacy class sizes, then N is nilpotent. In particular, we show that N is abelian or is the product of a p-group P by a central subgroup of G. ...
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Nilpotent and Abelian Hall Subgroups in Fintie Groups
American Mathematical Society (2015-07)We give a characterization of the finite groups having nilpotent or abelian Hall π-subgroups that can easily be verified using the character table.
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Normal subgroups and class sizes of elements of prime power order
American Mathematical Society (2012)If G is a finite group and N is a normal subgroup of G with two G-conjugacy class sizes of elements of prime power order, then we show that N is nilpotent.
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Normal subgroups and p-regular G-class sizes.
© 2011 Elsevier (2011-06)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 the Solvability of groups with four class sizes
World Scientific Publishing (2012)It is shown that if the set of conjugacy class sizes of a nite group G is f1; m; n;mng, where m; n are positive integers which do not divide each other, then G is up to central factors a fp; qg-group. In particular, G ...
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p-divisibility of conjugacy class sizes and normal p-complements
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 jxGj 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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Powers of conjugacy classes in a finite group
Springer (2019)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 concerning ...
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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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Some problems about products of conjugacy classes in finite groups
University of Isfahan (2019-03)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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Squares of real conjugacy classes in finite groups
Springer Verlag (2017-07)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 structure. ...
