Listar por tema "finite groups"
Mostrando ítems 1-10 de 10
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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 ... -
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. -
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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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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On powers of conjugacy classes in finite groups
De Gruyter (2022-03-17)Let 𝐾 and 𝐷 be conjugacy classes of a finite group 𝐺, and suppose that we have Kn=D∪D−1 for some integer n≥2. Under these assumptions, it was conjectured that ⟨K⟩ must be a (normal) solvable subgroup of 𝐺. Recently ...
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On the number of invariant Sylow subgroups under coprime action
Elsevier (2017-07)Let A and G be finite groups such that A acts coprimely on G via automorphisms. We study the number of A-invariant Sylow p-subgroups of G, say V a/p (G), for every prime p, and establish several arithmetical properties and ...
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Order of products of elements in finite groups
Wiley (2018-10)If G is a finite group, p is a prime, and x∈G, it is an interesting problem to place x in a convenient small (normal) subgroup of G, assuming some knowledge of the order of the products xy, for certain p‐elements y of G.
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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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Restrictions on maximal invariant subgroups implying solvability of finite groups
Springer Verlag (2018)Suppose that G and A are finite groups such that A acts coprimely on G via automorphisms. It is interesting to investigate the structure and properties of G when we impose some restrictions on its maximal A-invariant ...
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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. ...
