Results 1 to 10 of about 897 (256)
Partition numbers of finite solvable groups [PDF]
Advances in Group Theory and Applications, 2018 A group partition is a group cover in which the elements have trivial pairwise intersection. Here we define the partition number of a group - the minimal number of subgroups necessary to form a partition - and examine some of its properties, including ...
Tuval Foguel, Nick Sizemore
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Irredundant families of maximal subgroups of finite solvable groups [PDF]
International Journal of Group Theory, 2023 Let $\mathcal{M}$ be a family of maximal subgroups of a group $G.$ We say that $\mathcal{M}$ is irredundant if its intersection is not equal to the intersection of any proper subfamily of $\mathcal{M}$. The maximal dimension of $G$ is the maximal size of
Agnieszka Stocka
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Some criteria for solvability and supersolvability [PDF]
Journal of Mahani Mathematical Research, 2023 Denote by $ G $ a finite group, by $ {\rm hsn}(G) $ the harmonic mean Sylow number (eliminating the Sylow numbers that are one) in $G$ and by $ {\rm gsn}(G) $ the geometric mean Sylow number (eliminating the Sylow numbers that are one) in $G$.
Zohreh Habibi, Masoomeh Hezarjaribi
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Profinite just infinite residually solvable Lie algebras [PDF]
International Journal of Group Theory, 2023 We provide some characterization theorems about just infinite profinite residually solvable Lie algebras, similarly to what C. Reid has done for just infinite profinite groups.
Dario Villanis Ziani
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Finite non-solvable groups with few 2-parts of co-degrees of irreducible characters [PDF]
AUT Journal of Mathematics and Computing, 2023 For a character $ \chi $ of a finite group $ G $, the number $ \chi^c(1)=\frac{[G:{\rm ker}\chi]}{\chi(1)} $ is called the co-degree of $ \chi $. Let ${\rm Sol}(G)$ denote the solvable radical of $G$.
Neda Ahanjideh
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Diophantine problems in solvable groups [PDF]
Bulletin of Mathematical Sciences, 2020 We study the Diophantine problem (decidability of finite systems of equations) in different classes of finitely generated solvable groups (nilpotent, polycyclic, metabelian, free solvable, etc.), which satisfy some natural “non-commutativity” conditions.
Albert Garreta +2 more
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On homogeneous spaces with finite anti-solvable stabilizers
Comptes Rendus. Mathématique, 2022 We say that a group is anti-solvable if all of its composition factors are non-abelian. We consider a particular family of anti-solvable finite groups containing the simple alternating groups for $n\ne 6$ and all 26 sporadic simple groups. We prove that,
Lucchini Arteche, Giancarlo
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The minimum sum of element orders of finite groups [PDF]
International Journal of Group Theory, 2021 Let $ G $ be a finite group and \( \psi(G)=\sum_{g\in G}o(g) \), where $ o(g) $ denotes the order of $g\in G$. We show that the Conjecture 4.6.5 posed in [Group Theory and Computation, (2018) 59-90], is incorrect.
Maghsoud Jahani +3 more
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Some remarks on unipotent automorphisms [PDF]
International Journal of Group Theory, 2020 An automorphism $\alpha$ of the group $G$ is said to be $n$-unipotent if $[g,_n\alpha]=1$ for all $g\in G$. In this paper we obtain some results related to nilpotency of groups of $n$-unipotent automorphisms of solvable groups.
Orazio Puglisi, Gunnar Traustason
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Conjugacy Class Sizes in Affine Semi-linear Groups [PDF]
Advances in Group Theory and Applications, 2020 The aim of this work is to study the structure and sizes of conjugacy classes in certain affine semi-linear groups. This provides a wealth of finite groups of small conjugate rank that are solvable and non-nilpotent.
Hossein Shahrtash
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