Results 11 to 20 of about 8,796 (305)
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
doaj +1 more source
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
doaj +1 more source
Characterizations of Fitting p-Groups whose Proper Subgroups are Solvable [PDF]
Advances in Group Theory and Applications, 2017 This work continues the study of infinitely generated groups whose proper subgroups are solvable and in whose homomorphic images normal closures of finitely generated subgroups are residually nilpotent. In [4], it has been shown that such a group, if not
A.O. Asar
doaj +1 more source
Corrigendum to: “Characterizations of Fitting p-Groups whose Proper Subgroups are Solvable” [PDF]
Advances in Group Theory and Applications, 2017 The paper entitled "Characterizations of Fitting p-Groups whose Proper Subgroups are Solvable" (Adv. Group Theory Appl. 3 (2017), 31-53) contains a serious error. The proof of Lemma 2.8 relating to p=3 is false.
A.O. Asar
doaj +1 more source
Corrigendum II to: “Characterization of Fitting p-groups whose proper subgroups are solvable” [PDF]
Advances in Group Theory and Applications, 2018 Unfortunately “Corrigendum to Characterizations of Fitting p-groups whose proper subgroups are solvable” contains an error in the conclusion part of Lemma 2.1 (c).
A.O. Asar
doaj +1 more source
A note on finite groups with the indice of some maximal subgroups being primes [PDF]
International Journal of Group Theory, 2017 The Theorem 12 in [A note on $p$-nilpotence and solvability of finite groups, J. Algebra 321 (2009) 1555--1560.] investigated the non-abelian simple groups in which some maximal subgroups have primes indices. In this note we show that this
Cui Zhang
doaj +1 more source
SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS AND COMPLEXES [PDF]
Journal of Algebraic Systems, 2013 In this paper, we verify the solvability of free product of finite cyclic groups with topological methods. We use Cayley graphs and Everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator ...
Hanieh Mirebrahimi, Fatemeh Ghanei
doaj +1 more source
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
doaj +1 more source
Solvable Lie A-algebras. [PDF]
, 2011 A finite-dimensional Lie algebra $L$ over a field $F$ is called an $A$-algebra if all of its nilpotent subalgebras are abelian. This is analogous to the concept of an $A$-group: a finite group with the property that all of its Sylow subgroups are abelian.
Towers, David A., David A. Towers
core +1 more source
Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent [PDF]
International Journal of Group Theory, 2020 The main result of our consideration is the proof of the centrally nilpotency of class two property for connected topological proper loops $L$ of dimension $\le 3$ which have an at most six-dimensional solvable indecomposable Lie group as their ...
Agota Figula, Ameer Al-Abayechi
doaj +1 more source