Chong, Hip Kuen Wise, Daniel T.
Published in
Journal of Group Theory

We study a family of finitely generated residually finite groups. These groups are doubles F 2 * H F 2 F_{2}*_{H}F_{2} of a rank-2 free group F 2 F_{2} along an infinitely generated subgroup 𝐻. Varying 𝐻 yields uncountably many groups up to isomorphism.

Romero, Nadia
Published in
Journal of Group Theory

We explore conditions for the Frobenius–Wielandt morphism to commute with the operations of deflation and tensor induction on the Burnside ring. In doing this, we review the commutativity with induction. The techniques used for induction and tensor induction no longer work for deflation, so, in this case, we make use of tools coming from the theory...

Noseda, Francesco Snopce, Ilir
Published in
Journal of Group Theory

Let 𝑝 be a prime. We say that a pro-𝑝 group is self-similar of index p k p^{k} if it admits a faithful self-similar action on a p k p^{k} -ary regular rooted tree such that the action is transitive on the first level. The self-similarity index of a self-similar pro-𝑝 group 𝐺 is defined to be the least power of 𝑝, say p k p^{k} , such that 𝐺 is self...

Daws, Matthew
Published in
Journal of Group Theory

Assume that A ( G ) A(G) and B ( H ) B(H) are the Fourier and Fourier–Stieltjes algebras of locally compact groups 𝐺 and 𝐻, respectively. Ilie and Spronk have shown that continuous piecewise affine maps α : Y ⊆ H → G \alpha\colon Y\subseteq H\to G induce completely bounded homomorphisms Φ : A ( G ) → B ( H ) \Phi\colon A(G)\to B(H) and that...

Bannuscher, Falk Litterick, Alastair Uchiyama, Tomohiro
Published in
Journal of Group Theory

Let 𝑘 be a non-perfect separably closed field. Let 𝐺 be a connected reductive algebraic group defined over 𝑘. We study rationality problems for Serre’s notion of complete reducibility of subgroups of 𝐺. In particular, we present the first example of a connected non-abelian 𝑘-subgroup 𝐻 of 𝐺 that is 𝐺-completely reducible but not 𝐺-completely reduci...

Almazaydeh, Asma Ibrahim Macpherson, Dugald
Published in
Journal of Group Theory

We construct via Fraïssé amalgamation an 𝜔-categorical structure whose automorphism group is an infinite oligomorphic Jordan primitive permutation group preserving a “limit of 𝐷-relations”. The construction is based on a semilinear order whose elements are labelled by sets carrying a 𝐷-relation, with strong coherence conditions governing how these ...

Soto-Andrade, Jorge Yáñez-Valdés, Maria-Francisca
Published in
Journal of Group Theory

We show that the Gelfand character χ G \chi_{G} of a finite group 𝐺 (i.e. the sum of all irreducible complex characters of 𝐺) may be realized as a “twisted trace” g ↦ Tr ( ρ g ∘ T ) g\mapsto\operatorname{Tr}(\rho_{g}\circ T) for a suitable involutive linear automorphism 𝑇 of L 2 ( G ) L^{2}(G) , where ( L 2 ( G ) , ρ ) (L^{2}(G),\rho) is the ...

Chen, Jiyong Huang, Hong Yi
Published in
Journal of Group Theory

Let 𝐺 be a permutation group on a set Ω, and recall that a base for 𝐺 is a subset of Ω such that its pointwise stabiliser is trivial. In a recent paper, Burness and Giudici introduced the Saxl graph of 𝐺, denoted Σ ( G ) \Sigma(G) , with vertex set Ω and two vertices adjacent if and only if they form a base for 𝐺. If 𝐺 is transitive, then Σ ( G...

Carta, Ludo Fairbairn, Ben T.
Published in
Journal of Group Theory

A Beauville surface is defined by the action of a finite group (Beauville group) on the product of two compact Riemann surfaces. In this paper, we consider higher products and the possibility of a similar action by a finite group, which we call a generalised Beauville group; we prove several results regarding the existence and construction of infin...

Pham, Lam Zhang, Xin
Published in
Journal of Group Theory

Let S ⊂ GL n ( Z ) S\subset\mathrm{GL}_{n}(\mathbb{Z}) be a finite symmetric set. We show that if the Zariski closure of Γ = ⟨ S ⟩ \Gamma=\langle S\rangle is a product of special linear groups or a special affine linear group, then the diameter of the Cayley graph Cay ( Γ / Γ ( q ) , π q ( S ) ) \operatorname{Cay}(\Gamma/\Gamma(q),\pi_{q}(S...