General Matrix Groups [HB 19]

 

Changes:

• The database known as glnzgps has been withdrawn as it is superseded by the database of maximal finite subgroups of GL(n, Q).

New features:

• A very efficient algorithm has been implemented for computing the conjugacy classes of elements in a finite matrix group.
• The maximal normal p-subgroup of a finite matrix group may be found using the new function pCore.
• The function ChangeRing may now be applied to an infinite group. For example, it may be used to change the ring of an infinite group over the integers to a finite group over GF(2), say.
• A restricted version of LowIndexSubgroups developed by Leedham-Green and O'Brien is now available for matrix groups.
• The new function ElementaryAbelianQuotient returns the p-elementary abelian quotient of a permutation group for a given prime p.
• A database of maximal finite subgroups of GL(n, Q) of degree up to 31 constructed by G. Nebe has been installed (RationalMatrixGroupDatabase).
• A database of the finite absolutely irreducible subgroups of $\mbox{\rm GL}_n({\cal D})$ where ${\cal D}$ is a definite quaternion algebra whose centre has degree d over $\mbox{\bf Q}$ and $nd\leq10$ has been installed. This collection is due to G. Nebe.

Bug fixes:

• Bug fixes have been made to the functions CosetTable, PCGroup, ClassMap and IsFinite.
• Errors in the generators for two exceptional groups of Lie type, namely E₆ and F₄, have been corrected. The errors were discovered by G. Malle.