Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Carmine Monetta"'
Publikováno v:
International Journal of Group Theory, Vol 13, Iss 4, Pp 351-367 (2023)
Let $\Gamma_G$ denote a graph associated with a group $G$. A compelling question about finite groups asks whether or not a finite group $H$ must be nilpotent provided $\Gamma_H$ is isomorphic to $\Gamma_G$ for a finite nilpotent group $G$. In the pre
Externí odkaz:
https://doaj.org/article/57a9ee5c8af14c57bfd0e27cf51d197f
Autor:
Raimundo Bastos, Carmine Monetta
Publikováno v:
International Journal of Group Theory, Vol 12, Iss 2, Pp 111-121 (2023)
This is a survey on a group construction in connection with the non-abelian tensor square of groups. We report on the developments obtained in the last decade emphasizing the results from a commutator point of view.
Externí odkaz:
https://doaj.org/article/5184f28e61454f47bb3c79e3e10717b6
Autor:
Raimundo Bastos, Carmine Monetta
Publikováno v:
International Journal of Group Theory, Vol 10, Iss 4, Pp 187-195 (2021)
Let $n$ be a positive integer and let $G$ be a group. We denote by $\nu(G)$ a certain extension of the non-abelian tensor square $G \otimes G$ by $G \times G$. Set $T_{\otimes}(G) = \{g \otimes h \mid g,h \in G\}$. We prove that if
Externí odkaz:
https://doaj.org/article/1ee5614747af4f14b40261809ff36213
Autor:
S. Camp-Mora, Carmine Monetta
Publikováno v:
Archiv der Mathematik. 115:131-137
A subgroup H of a group G is said to be complemented in G if there exists a subgroup K of G such that $$G=HK$$ and $$H \cap K=1$$ . We prove that, for a locally soluble group G, all cyclic subgroups are complemented if and only if it is the semidirec
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2fd805d78bed5651d8f1dd14fcc8a4bd
https://doi.org/10.1007/s00013-020-01473-0
https://doi.org/10.1007/s00013-020-01473-0
Let $G$ be a finite group, let $p$ be a prime and let $w$ be a group-word. We say that $G$ satisfies $P(w,p)$ if the prime $p$ divides the order of $xy$ for every $w$-value $x$ in $G$ of $p'$-order and for every non-trivial $w$-value $y$ in $G$ of or
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::281ca73598a294770245e54f76db15a4
Let $G$ be a finite $p$-group. In this paper we obtain bounds for the exponent of the non-abelian tensor square $G \otimes G$ and of $\nu(G)$, which is a certain extension of $G \otimes G$ by $G \times G$. In particular, we bound $\exp(\nu(G))$ in te
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::12d6067bdeabf1cf47efacb01eaf95bd
http://arxiv.org/abs/2007.10693
http://arxiv.org/abs/2007.10693
Autor:
Carmine Monetta, Raimundo Bastos
Let $G$ be a finite group and let $k \geq 2$. We prove that the coprime subgroup $\gamma_k^*(G)$ is nilpotent if and only if $|xy|=|x||y|$ for any $\gamma_k^*$-commutators $x,y \in G$ of coprime orders (Theorem A). Moreover, we show that the coprime
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::47e2dbbfc155940ff971760168463c50
http://hdl.handle.net/11386/4750650
http://hdl.handle.net/11386/4750650
We prove that the kth term of the lower central series of a finite group G is nilpotent if and only if | a b | = | a | | b | {|ab|=|a||b|} for any γ k {\gamma_{k}} -commutators a , b ∈ G {a,b\in G} of coprime orders.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::131582180bd4b09335017d857c8839a8
http://arxiv.org/abs/1706.03133
http://arxiv.org/abs/1706.03133
Autor:
GRAZIAN, VALENTINA1 valentina.grazian@unimib.it, LUCCHINI, ANDREA2 lucchini@math.unipd.it, MONETTA, CARMINE3 cmonetta@unisa.it
Publikováno v:
International Journal of Group Theory. Dec2024, Vol. 13 Issue 4, p351-367. 17p.
Autor:
BASTOS, RAIMUNDO1 bastos@mat.unb.br, MONETTA, CARMINE2 cmonetta@unisa.it
Publikováno v:
International Journal of Group Theory. Summer2023, Vol. 12 Issue 2, p111-121. 11p.