Csaba Schneider

Six-dimensional nilpotent Lie algebras

Abstract We give a full classification of six-dimensional nilpotent Lie algebras over an arbitrary field, including fields that are not algebraically closed and fields of characteristic 2. To achieve the classification we use the action of the automorphism group on the second cohomology space, as isomorphism types of nilpotent Lie algebras correspond to orbits of subspaces under this action. In some cases, these orbits are determined using geometric invariants, such as the Gram determinant or the Arf invariant. As a byproduct, we completely determine, for a four-dimensional vector space V , the orbits of GL ( V ) on the set of two-dimensional subspaces of V ∧ V .

A computer-based approach to the classification of nilpotent Lie algebras

We adapt the p-group generation algorithm to classify smalldimensional nilpotent Lie algebras over small fields. Using an implementation of this algorithm, we list the nilpotent Lie algebras of dimension up to 9 over 𝔽2 and those of dimension up to 7 over 𝔽3 and 𝔽5.

The rank of the semigroup of transformations stabilising a partition of a finite set

Let

Innately transitive subgroups of wreath products in product action

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Factorisations of characteristically simple groups

be a partition of a finite set X . We say that a transformation f : X → X preserves (or stabilises) the partition

Primitive flag-transitive generalized hexagons and octagons

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Constructive membership testing in black-box classical groups

if for all P ∈

ELATION GENERALIZED QUADRANGLES FOR WHICH THE NUMBER OF LINES ON A POINT IS THE SUCCESSOR OF A PRIME

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Generalised Sifting in Black-Box Groups

there exists Q ∈

Groups of prime-power order with a small second derived quotient

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