9 citations · 53 across the 12 of their papers we have counts for
12 papers
Relative Rota-Baxter groups and skew left braces
Nishant Rathee, Mahender Singh
Relative Rota-Baxter groups are generalisations of Rota-Baxter groups and introduced recently in the context of Lie groups. In this paper, we explore connections of relative Rota-B…
Commutator subgroups and crystallographic quotients of virtual extensions of symmetric groups
Pravin Kumar, Tushar Kanta Naik, Neha Nanda +1
The virtual braid group , the virtual twin group and the virtual triplet group are extensions of the symmetric group , which are motivated by the Alexander…
Generalised Legendrian racks of Legendrian links
Biswadeep Karmakar, Deepanshi Saraf, Mahender Singh
A generalised Legendrian rack is a rack equipped with a Legendrian structure, which is a pair of maps encoding the information of Legendrian Reidemeister moves together with up and…
Congruence subgroups and crystallographic quotients of small Coxeter groups
Pravin Kumar, Tushar Kanta Naik, Mahender Singh
Small Coxeter groups are precisely the ones for which the Tits representation is integral, which makes the study of their congruence subgroups relevant. The symmetric group h…
Finiteness of canonical quotients of Dehn quandles of surfaces
Neeraj K. Dhanwani, Mahender Singh
The Dehn quandle of a closed orientable surface is the set of isotopy classes of non-separating simple closed curves with a natural quandle structure arising from Dehn twists. In t…
Enhancements of link colorings via idempotents of quandle rings
Mohamed Elhamdadi, Brandon Nunez, Mahender Singh
We show that quandle rings and their idempotents lead to proper enhancements of the well-known quandle coloring invariant of links in the 3-space. We give explicit examples to show…
Idempotents, free products and quandle coverings
Mohamed Elhamdadi, Brandon Nunez, Mahender Singh +1
In this paper, we investigate idempotents in quandle rings and relate them with quandle coverings. We prove that integral quandle rings of quandles of finite type that are non-triv…
Presentations of Dehn quandles
Neeraj K. Dhanwani, Hitesh Raundal, Mahender Singh
The paper gives two approaches to write explicit presentations for the class of Dehn quandles using presentations of their underlying groups. The first approach gives finite presen…
Orderability of link quandles
Hitesh Raundal, Mahender Singh, Manpreet Singh
The paper develops a general theory of orderability of quandles with a focus on link quandles of tame links and gives some general constructions of orderable quandles. We prove tha…
Structure and automorphisms of pure virtual twin groups
Tushar Kanta Naik, Neha Nanda, Mahender Singh
Study of stable isotopy classes of a finite collection of immersed circles without triple or higher intersections on closed oriented surfaces is considered as a planar analogue of…
Link quandles are residually finite
Valeriy G. Bardakov, Mahender Singh, Manpreet Singh
Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work [2] residual finiteness of…
Free quandles and knot quandles are residually finite
Valeriy G. Bardakov, Mahender Singh, Manpreet Singh
In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residu…