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On the recognizability of some projective general linear groups by the prime graph

Masoumeh Sajjadi (2022)

Commentationes Mathematicae Universitatis Carolinae

Let G be a finite group. The prime graph of G is a simple graph Γ ( G ) whose vertex set is π ( G ) and two distinct vertices p and q are joined by an edge if and only if G has an element of order p q . A group G is called k -recognizable by prime graph if there exist exactly k nonisomorphic groups H satisfying the condition Γ ( G ) = Γ ( H ) . A 1-recognizable group is usually called a recognizable group. In this problem, it was proved that PGL ( 2 , p α ) is recognizable, if p is an odd prime and α > 1 is odd. But for even α , only the recognizability...

On the representation theory of braid groups

Ivan Marin (2013)

Annales mathématiques Blaise Pascal

This work presents an approach towards the representation theory of the braid groups B n . We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids, with the help of Drinfeld associators. We set a dictionary between representation-theoretic properties of these two structures, and tools to describe the representations thus obtained. We give an explanation for the frequent apparition of unitary structures on classical...

On the resolvability of Hall triple systems

Martin Oxenham, Rey Casse (1998)

Bollettino dell'Unione Matematica Italiana

È ben noto che fra le classi di sistemi ternari di Hall (HTS), gli HTS Abeliani ammettano una risoluzione siccome sono esattamente gli spazi affini finiti d'ordine 3; per questi sistemi una tal risoluzione è fornita dalla relazione di parallelismo. In questa nota viene dimostrato che certe classi di HTS non Abeliani costrutti dai gruppi di Burnside B 3 , r , r 3 anche ammettono una risoluzione. Allora, questi esempi di HTS si possono considerare anche come spazi finiti di Sperner e dunque la nota conclude...

On the saturated numerical semigroups

Sedat Ilhan, Meral Süer (2016)

Open Mathematics

In this study, we characterize all families of saturated numerical semigroups with multiplicity four. We also present some results about invariants of these semigroups.

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