The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Mark L Lewis - One of the best experts on this subject based on the ideXlab platform.
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Nonsolvable Groups with no Prime Dividing Four Character Degrees
Algebras and Representation Theory, 2017Co-Authors: Mehdi Ghaffarzadeh, Mark L Lewis, Mohsen Ghasemi, Hung P. Tong-vietAbstract:Given a finite group G , we say that G has property
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finite groups with an Irreducible Character of large degree
Manuscripta Mathematica, 2016Co-Authors: Nguyen Ngoc Hung, Mark L LewisAbstract:Let G be a finite group and d the degree of a complex Irreducible Character of G, then write |G| = d(d + e) where e is a nonnegative integer. We prove that |G| ≤ e 4−e 3 whenever e > 1. This bound is best possible and improves on several earlier related results.
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finite groups with an Irreducible Character of large degree
arXiv: Group Theory, 2015Co-Authors: Nguyen Ngoc Hung, Mark L LewisAbstract:Let $G$ be a finite group and $d$ the degree of a complex Irreducible Character of $G$, then write $|G|=d(d+e)$ where $e$ is a nonnegative integer. We prove that $|G|\leq e^4-e^3$ whenever $e>1$. This bound is best possible and improves on several earlier related results.
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bounding the number of Irreducible Character degrees of a finite group in terms of the largest degree
Journal of Algebra and Its Applications, 2014Co-Authors: Mark L Lewis, Alexander MoretoAbstract:We conjecture that the number of Irreducible Character degrees of a finite group is bounded in terms of the number of prime factors (counting multiplicities) of the largest Character degree. We prove that this conjecture holds when the largest Character degree is prime and when the Character degree graph is disconnected.
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Taketa’s theorem for some Character degree sets
Archiv der Mathematik, 2013Co-Authors: Kamal Aziziheris, Mark L LewisAbstract:Let cd (G) be the set of Irreducible complex Character degrees of a finite group G . The Taketa problem conjectures that if G is a finite solvable group, then $${{\rm dl}(G) \leqslant |{\rm cd} (G)|}$$ , where dl( G ) is the derived length of G . In this note, we show that this inequality holds if either all nonlinear Irreducible Characters of G have even degrees or all Irreducible Character degrees are odd. Also, we prove that this inequality holds if all Irreducible Character degrees have exactly the same prime divisors. Finally, Isaacs and Knutson have conjectured that the Taketa problem might be true in a more general setting. In particular, they conjecture that the inequality $${{\rm dl}(N) \leqslant |{\rm cd} {(G \mid N)}|}$$ holds for all normal solvable subgroups N of a group G . We show that this conjecture holds if $${{\rm cd} {(G \mid N')}}$$ is a set of non-trivial p –powers for some fixed prime p .
Abolfazl Tehranian - One of the best experts on this subject based on the ideXlab platform.
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Characterization of textit pgl 2 p 2 pgl 2 p2 by order and some Irreducible Character degrees
Bulletin of The Iranian Mathematical Society, 2019Co-Authors: Ali Iranmanesh, Mozhgan Mokhtari, Abolfazl TehranianAbstract:In this paper, we determine all of finite groups whose order and the largest of their Irreducible Character degrees are the same as $${\textit{PGL}}( 2 , p^{2} ) $$ for all odd prime numbers p. As a consequence, we show that the groups $${\textit{PGL}}( 2 , p^{2} ) $$ are uniquely determined by the structure of their complex group algebras.
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Characterization of $${\textit{PGL}}(2 , p^{2} ) $$PGL(2,p2) by Order and Some Irreducible Character Degrees
Bulletin of the Iranian Mathematical Society, 2019Co-Authors: Ali Iranmanesh, Mozhgan Mokhtari, Abolfazl TehranianAbstract:In this paper, we determine all of finite groups whose order and the largest of their Irreducible Character degrees are the same as $${\textit{PGL}}( 2 , p^{2} ) $$ PGL ( 2 , p 2 ) for all odd prime numbers p . As a consequence, we show that the groups $${\textit{PGL}}( 2 , p^{2} ) $$ PGL ( 2 , p 2 ) are uniquely determined by the structure of their complex group algebras.
I M Isaacs - One of the best experts on this subject based on the ideXlab platform.
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upper bounds for the number of Irreducible Character degrees of a group
Journal of Algebra, 2014Co-Authors: I M IsaacsAbstract:Abstract Let G be a p-solvable group for some prime p, and suppose that the largest Irreducible Character degree of G is kp, where k p is an integer. We obtain an upper bound on the total number of different Irreducible Character degrees of G, where the bound depends on k but not on p.
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the average degree of an Irreducible Character of a finite group
Israel Journal of Mathematics, 2013Co-Authors: I M Isaacs, Maria Loukaki, Alexander MoretoAbstract:Given a finite group G, we write acd(G) to denote the average of the degrees of the Irreducible Characters of G. We show that if acd(G) ≤ 3, then G is solvable. Also, if acd(G) < 3/2, then G is supersolvable, and if acd(G) < 4/3, then G is nilpotent.
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Groups whose real Irreducible Characters have degrees coprime to p
Journal of Algebra, 2012Co-Authors: I M Isaacs, Gabriel NavarroAbstract:Abstract In this paper we study groups for which every real Irreducible Character has degree not divisible by some given odd prime p .
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p -groups having few almost-rational Irreducible Characters
Israel Journal of Mathematics, 2011Co-Authors: I M Isaacs, Gabriel Navarro, Josu SangronizAbstract:We prove that a 2-group has exactly five rational Irreducible Characters if and only if it is dihedral, semidihedral or generalized quaternion. For an arbitrary prime p, we say that an Irreducible Character χ of a p-group G is “almost rational” if ℚ(χ) is contained in the cyclotomic field ℚ p , and we write ar(G) to denote the number of almost-rational Irreducible Characters of G. For noncyclic p-groups, the two smallest possible values for ar(G) are p 2 and p 2 + p − 1, and we study p-groups G for which ar(G) is one of these two numbers. If ar(G) = p 2 + p − 1, we say that G is “exceptional”. We show that for exceptional groups, |G: G′| = p 2, and so the assertion about 2-groups with which we began follows from this. We show also that for each prime p, there are exceptional p-groups of arbitrarily large order, and for p ≥ 5, there is a pro-p-group with the property that all of its finite homomorphic images of order at least p 3 are exceptional.
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finite group elements where no Irreducible Character vanishes
Journal of Algebra, 1999Co-Authors: I M Isaacs, Gabriel Navarro, Thomas R WolfAbstract:In this paper, we consider elements x of a finite group G with the property that χ(x) ≠ 0 for all Irreducible Characters χ of G. If G is solvable and x has odd order, we show that x must lie in the Fitting subgroup F(G).
Lucia Morotti - One of the best experts on this subject based on the ideXlab platform.
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Sign conjugacy classes of the alternating groups
Communications in Algebra, 2017Co-Authors: Lucia MorottiAbstract:ABSTRACTA conjugacy class C of a finite group G is a sign conjugacy class if every Irreducible Character of G takes value 0,1 or −1 on C. In this paper, we classify the sign conjugacy classes of alternating groups.
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Sign conjugacy classes of the symmetric groups
arXiv: Combinatorics, 2014Co-Authors: Lucia MorottiAbstract:A conjugacy class $C$ of a finite group $G$ is a sign conjugacy class if every Irreducible Character of $G$ takes value 0, 1 or -1 on $C$. In this paper we classify the sign conjugacy classes of the symmetric groups and thereby verify a conjecture of Olsson.
Ali Iranmanesh - One of the best experts on this subject based on the ideXlab platform.
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Characterization of textit pgl 2 p 2 pgl 2 p2 by order and some Irreducible Character degrees
Bulletin of The Iranian Mathematical Society, 2019Co-Authors: Ali Iranmanesh, Mozhgan Mokhtari, Abolfazl TehranianAbstract:In this paper, we determine all of finite groups whose order and the largest of their Irreducible Character degrees are the same as $${\textit{PGL}}( 2 , p^{2} ) $$ for all odd prime numbers p. As a consequence, we show that the groups $${\textit{PGL}}( 2 , p^{2} ) $$ are uniquely determined by the structure of their complex group algebras.
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Characterization of $${\textit{PGL}}(2 , p^{2} ) $$PGL(2,p2) by Order and Some Irreducible Character Degrees
Bulletin of the Iranian Mathematical Society, 2019Co-Authors: Ali Iranmanesh, Mozhgan Mokhtari, Abolfazl TehranianAbstract:In this paper, we determine all of finite groups whose order and the largest of their Irreducible Character degrees are the same as $${\textit{PGL}}( 2 , p^{2} ) $$ PGL ( 2 , p 2 ) for all odd prime numbers p . As a consequence, we show that the groups $${\textit{PGL}}( 2 , p^{2} ) $$ PGL ( 2 , p 2 ) are uniquely determined by the structure of their complex group algebras.
