Automorphism groups of quandles arising from groups

Valeriy G. Bardakov, Pinka Dey, Mahender Singh

Результат исследования: Научные публикации в периодических изданияхстатья

7 Цитирования (Scopus)

Аннотация

Let G be a group and φ∈ Aut (G). Then the set G equipped with the binary operation a∗ b= φ(ab- 1) b gives a quandle structure on G, denoted by Alex (G, φ) , and called the generalised Alexander quandle of G with respect to φ. When G is an additive abelian group and φ= - id G, then Alex (G, φ) is the well-known Takasaki quandle of G. In this paper, we determine the group of automorphisms and inner automorphisms of Takasaki quandles of abelian groups with no 2-torsion, and Alexander quandles of finite abelian groups with respect to fixed-point free automorphisms. As an application, we prove that if G≅ (Z/ pZ) n and φ is multiplication by a non-trivial unit of Z/ pZ, then Aut (Alex (G, φ)) acts doubly transitively on Alex (G, φ). This generalises a recent result of Ferman et al. (J Knot Theory Ramifications 20:463–468, 2011) for quandles of prime order.

Язык оригиналаанглийский
Страницы (с-по)519-530
Число страниц12
ЖурналMonatshefte fur Mathematik
Том184
Номер выпуска4
DOI
СостояниеОпубликовано - 1 дек 2017

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