Zobrazeno 1 - 10
of 347
pro vyhledávání: '"20D45"'
Autor:
Zhang, Huhu, Gao, Xing
Rota-Baxter operators on groups were studied quite recently. Motivated mainly by the fact that weight zero Rota-Baxter operators and averaging operators are Koszul dual to each other, we propose the concepts of averaging group and averaging Hopf alge
Externí odkaz:
http://arxiv.org/abs/2412.11600
Autor:
Glasby, Stephen P.
We give a complete and irredundant list of the finite groups $G$ for which Aut$(G)$, acting naturally on $G$, has precisely $3$ orbits. There are 7 infinite families: one abelian, one non-nilpotent, three families of non-abelian $2$-groups and two fa
Externí odkaz:
http://arxiv.org/abs/2411.11273
We prove that the Parker--Semeraro systems satisfy six of the nine Kessar--Linckelmann--Lynd--Semeraro weight conjectures for saturated fusion systems. As a by-product we obtain that Robinson's ordinary weight conjecture holds for the principal $3$-b
Externí odkaz:
http://arxiv.org/abs/2407.07211
Autor:
Nicotera, Chiara
We consider groups $G$ such that the set $[G,\varphi]=\{g^{-1}g^{\varphi}|g\in G\}$ is a subgroup for every automorphism $\varphi$ of $G$, and we prove that there exists such a group $G$ that is finite and nilpotent of class $n$ for every $n\in\mathb
Externí odkaz:
http://arxiv.org/abs/2405.08433
For a subgroup $S$ of a group $G$, let $I_G(S)$ denote the set of commutators $[g,s]=g^{-1}g^s$, where $g\in G$ and $s\in S$, so that $[G,S]$ is the subgroup generated by $I_G(S)$. We prove that if $G$ is a $p$-soluble finite group with a Sylow $p$-s
Externí odkaz:
http://arxiv.org/abs/2404.14599
Autor:
Crespo, Teresa
We consider relatively prime integer numbers $m$ and $n$ such that each group of order $mn$ has a normal subgroup of order $m$. We prove that each brace of size $mn$ is a semidirect product of a brace of size $m$ and a brace of size $n$. We further g
Externí odkaz:
http://arxiv.org/abs/2401.16892
Autor:
Li, Cai Heng, Zhu, Yan Zhou
Publikováno v:
Proc. Lond. Math. Soc. (3) 129 (2024), no. 5, Paper No. e70002
Building upon previous results, a classification is given of finite $p$-groups of which subgroups of order $p$ are all fused. This completes the classification problem dated back to Higman 1963 on the so-called Suzuki $2$-groups, and confirms a conje
Externí odkaz:
http://arxiv.org/abs/2312.16416
Autor:
Tertooy, Sam
Publikováno v:
Topology and its Applications (2024), 109089
We extend the notions of "$R_\infty$-property" and "full (extended) Reidemeister spectrum" to finite groups in a meaningful way. We provide examples of finite groups admitting these properties, if they exist, by looking at groups of small order as we
Externí odkaz:
http://arxiv.org/abs/2311.12594
Autor:
A, Sivaranjani, S, Radha
Paley graphs are Cayley graphs which are circulant and strongly regular. Paley-type graph of order a product of two distinct Pythagorean primes was introduced by Dr Angsuman Das. In this paper, we extend the study of Paley-type graphs to the order a
Externí odkaz:
http://arxiv.org/abs/2310.04137
Autor:
de Melo, Emerson, Caldeira, Jhone
Let $A$ be a non-metacyclic finite group. Suppose that $A$ acts coprimely on a finite group $G$ in such a manner that $C_G(a)$ is nilpotent for any $a\in A^{\#}$. In the present paper we investigate some conditions on $A$ which imply that $G$ is nilp
Externí odkaz:
http://arxiv.org/abs/2305.07177