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pro vyhledávání: '"P. Delizia"'
The study of verbal subgroups within a group is well-known for being an effective tool to obtain structural information about a group. Therefore, conditions that allow the classification of words in a free group are of paramount importance. One of th
Externí odkaz:
http://arxiv.org/abs/2404.06308
In this paper we revisit the description of all verbal subgroups of the group of automorphisms of a regular rooted tree $\mathcal{T}_d$, for $d>2$ and odd.
Externí odkaz:
http://arxiv.org/abs/2402.08501
The solubility graph $\Gamma_S(G)$ associated with a finite group $G$ is a simple graph whose vertices are the elements of $G$, and there is an edge between two distinct vertices if and only if they generate a soluble subgroup. In this paper, we focu
Externí odkaz:
http://arxiv.org/abs/2202.09563
Autor:
Costantino Delizia, Chiara Nicotera
Publikováno v:
International Journal of Group Theory, Vol 12, Iss 1, Pp 21-26 (2023)
We completely describe the structure of locally (soluble-by-finite) groups in which all abelian subgroups are locally cyclic. Moreover, we prove that Engel groups with the above property are locally nilpotent.
Externí odkaz:
https://doaj.org/article/5092643960854c6eac1932a1ec96fe7a
Akademický článek
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We show that there is a positive constant $\delta < 1$ such that the probability of satisfying either the $2$-Engel identity $[X_1, X_2, X_2] = 1$ or the metabelian identity $[[X_1, X_2], [X_3, X_4]] = 1$ in a finite group is either $1$ or at most $\
Externí odkaz:
http://arxiv.org/abs/1809.02997
We study the class of groups having the property that every non-nilpotent subgroup is equal to its normalizer. These groups are either soluble or perfect. We completely describe the structure of soluble groups and finite perfect groups with the above
Externí odkaz:
http://arxiv.org/abs/1705.06265
We study groups having the property that every non-abelian subgroup is equal to its normalizer. This class of groups is closely related to an open problem posed by Berkovich. We give a full classification of finite groups having the above property. W
Externí odkaz:
http://arxiv.org/abs/1607.07366
Locally finite groups having the property that every non-cyclic subgroup contains its centralizer are completely classified.
Comment: 12 pages
Comment: 12 pages
Externí odkaz:
http://arxiv.org/abs/1606.01669
Publikováno v:
Journal of Algebra 462 (2016), 23--36
We study groups having the property that every non-abelian subgroup contains its centralizer. We describe various classes of infinite groups in this class, and address a problem of Berkovich regarding the classification of finite $p$-groups with the
Externí odkaz:
http://arxiv.org/abs/1510.06545