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Permutations which make transitive groups primitive

Pedro Lopes (2009)

Open Mathematics

In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a subset of its generators such that these generators alone (the so-called primitive generators) imply the group is primitive. The remaining generators ensure transitivity or comply with specific features of the group. We show that, other than the symmetric and alternating groups, there are infinitely many primitive groups with one primitive generator each. These primitive groups...

Regular permutation sets and loops

Rita Capodaglio (2003)

Bollettino dell'Unione Matematica Italiana

Two suitable composition laws are defined in a regular permutation set in order to find new characterizations of some important classes of loops.

Weakly-exceptional quotient singularities

Dmitrijs Sakovics (2012)

Open Mathematics

A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow-up. In dimension 2, V. Shokurov proved that weakly-exceptional quotient singularities are exactly those of types D n, E 6, E 7, E 8. This paper classifies the weakly-exceptional quotient singularities in dimensions 3 and 4.

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