We study the virtually generating graph of pro-$p$ groups. We show that various classes of pro-$p$ groups have connected virtually generating graph and we bound its diameter in these cases; e.g.\ compact subgroups of analytic groups over local fields and the Nottingham group.
It is an open problem to determine whether surface groups can embed in Thompson's group $V$. We prove that any finitely generated subgroup of Thompson's group $T$ without abelian groups of arbitrary high rank is either virtually abelian or virtually free. In particular, surface groups don't embed in $T$, answering a qu...
Power graphs of groups and semigroups constitute a significant class of graphs in algebraic graph theory, bridging algebraic structures and graph theoretic concepts. Further, labeling of graphs, particularly those endowed with an algebraic structure as their vertex set, is a vibrant area of research. This article contr...
Gurvinder Singh, Neeraj Takshak, Amit Sehgal et al.· Journal of the Indonesian Ma...· 0 citations
An action of a group is binary if it induces the group of automorphisms of some homogeneous edge-coloured directed graph. In this paper we study the quasisimple groups $G$ with $G/Z(G)$ a sporadic simple group---we produce a complete classification of their binary actions.
In this article, we prove the Defect Conjecture for Cayley graphs of abelian groups, dihedral groups, and groups of the form $\mathbb{Z}/p\mathbb{Z} \rtimes \mathbb{Z}/(p-1)\mathbb{Z}$ where $p\geq 3$ is a prime. We also compute the Iwasawa invariants of the Bowen--Franks groups associated with these graphs in several...
Debanjana Kundu, Katharina Müller, A. Newton et al.· 0 citations
We explicitly describe polars of $Pin^c$ groups and related compact Lie groups and realize all of oriented real Grassmann manifolds as polars in $Pin^c$ groups.
H. Tasaki· Tohoku mathematical journal· 0 citations
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