Related papers: Strongly real special 2-groups

Let $ G $ be a finite group of order $ n$. The strong power graph $\mathcal{P}_s(G) $ of $G$ is the undirected graph whose vertices are the elements of $G$ such that two distinct vertices $a$ and $b$ are adjacent if $a^{{m}_1}$=$b^{{m}_2}$…

We give a group theoretic proof of the splitting of sharply 2-transitive groups of characteristic 3.

We present an explicit formula for subregular characters (i.e, irreducible finite-dimensional complex characters of submaximal degree) of the unitriangular group over a finite field of sufficiently large characteristic.

This exposition examines the theory of orthogonal groups and their subgroups over fields of positive characteristic, which has recently been used as an important tool in the study of automorphic forms and Langlands functionality. We present…

We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…

We construct parameterized families of imaginary (resp. real) quadratic fields whose class groups have $n$-rank at least $2$.

We describe the groups that have the same holomorph as a finite perfect group. Our results are complete for centerless groups. When the center is non-trivial, some questions remain open. The peculiarities of the general case are illustrated…

We show that double cosets of the infinite symmetric group with respect to some special subgroups admit natural structures of semigroups. We interpret elements of such semigroups in combinatorial terms (chips, colored graphs,…

We characterize when a generalized Baumslag-Solitar group is linear, and extend the result to the fundamental groups of a graph of groups with infinite virtually cyclic vertex and edge groups.

We relativise double categories of relations to stable orthogonal factorisation systems. Furthermore, we present the characterisation of the relative double categories of relations in two ways. The first utilises a generalised comprehension…

We present a characterization of the finite groups in which all real classes have prime powers size.

We give an explicit construction of sharply $2$-transitive groups with fixed point free involutions and without nontrivial abelian normal subgroup.

A strict 2-group is a 2-category with one object in which all morphisms and all 2-morphisms have inverses. 2-Groups have been studied in the context of homotopy theory, higher gauge theory and Topological Quantum Field Theory (TQFT). In the…

We present two distinct families of imaginary biquadratic fields, each of which contains infinitely many members, with each member having large class groups. Construction of the first family involves elliptic curves and their quadratic…

We define formal orbifolds over an algebraically closed field of arbitrary characteristic as curves together with some branch data. Their \'etale coverings and their fundamental groups are also defined. These fundamental group approximates…

We introduce and motivate the definition of the virtual Rokhlin property for topological groups. We then classify the 2-manifolds whose homeomorphism groups have the virtual Rokhlin property. We also establish the analogous result for…

We characterize the strong metric dimension of the power graph of a finite group. As applications, we compute the strong metric dimension of the power graph of a cyclic group, an abelian group, a dihedral group or a generalized quaternion…

A strong Gelfand pair (G,H) is a group G together with a subgroup H such that every irreducible character of H induces a multiplicity-free character of G. We classify the strong Gelfand pairs of the special linear groups SL(2, p) where p is…

This paper concerns finite groups of class (at most) two and of odd prime exponent $p$. Such a group is called special if the center lies within its derived group. Every group of class 2 and exponent $p$ can be uniquely expressed as the…

We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.