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Permutations which make transitive groups primitive

100%

Lopes P.

Open Mathematics

2009

tom 7

nr 4

650-659

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 are certain Mathieu groups, certain projective general and projective special linear groups, and certain subgroups of some affine special linear groups.

Weakly-exceptional quotient singularities

68%

Sakovics D.

Open Mathematics

2012

tom 10

nr 3

885-902

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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2 Open Mathematics

1 Lopes P.

1 Sakovics D.

1 2012

1 2009

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Permutations which make transitive groups primitive

Weakly-exceptional quotient singularities