A classification of nilpotent $۳$-BCI groups
عنوان مقاله: A classification of nilpotent $۳$-BCI groups
شناسه ملی مقاله: JR_THEGR-8-2_002
منتشر شده در در سال 1398
شناسه ملی مقاله: JR_THEGR-8-2_002
منتشر شده در در سال 1398
مشخصات نویسندگان مقاله:
Hiroki Koike - National Autonomous University of Mexico
Istvan Kovacs - University of Primorska
خلاصه مقاله:
Hiroki Koike - National Autonomous University of Mexico
Istvan Kovacs - University of Primorska
Given a finite group $G$ and a subset $S\subseteq G,$ the bi-Cayley graph $\bcay(G,S)$ is the graph whose vertex set is $G \times \{۰,۱\}$ and edge set is $\{ \{(x,۰),(s x,۱)\} : x \in G, s\in S \}$. A bi-Cayley graph $\bcay(G,S)$ is called a BCI-graph if for any bi-Cayley graph $\bcay(G,T),$ $\bcay(G,S) \cong \bcay(G,T)$ implies that $T = g S^\alpha$ for some $g \in G$ and $\alpha \in \aut(G)$. A group $G$ is called an $m$-BCI-group if all bi-Cayley graphs of $G$ of valency at most $m$ are BCI-graphs. It was proved by Jin and Liu that, if $G$ is a $۳$-BCI-group, then its Sylow $۲$-subgroup is cyclic, or elementary abelian, or $\Q$ [European J. Combin. ۳۱ (۲۰۱۰) ۱۲۵۷--۱۲۶۴], and that a Sylow $p$-subgroup, $p$ is an odd prime, is homocyclic [Util. Math. ۸۶ (۲۰۱۱) ۳۱۳--۳۲۰]. In this paper we show that the converse also holds in the case when $G$ is nilpotent, and hence complete the classification of nilpotent $۳$-BCI-groups.
کلمات کلیدی: bi-Cayley graph, BCI-group, graph isomorphism
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1194953/