## Programs
## Authors
## Contacts |
## ANU Polycyclic Quotient ProgramsAll three programs are available from the archive of the Algebra Program at the Mathematical Sciences Institute. The algorithms, details of the implementations and results obtained with the programs are described in the list of publications and their references. This program implements - the
*p*-quotient algorithm - the
*p*-group generation algorithm - an algorithm to decide isomorphism of
*p*-groups - an algorithm to compute the automorphism group of a
*p*-group
It has been used to obtain results such as: - there are 56092 groups of order 256
- the largest finite group generated by 3 elements
in which every element has order dividing 5 has order
5
^{2822}. - and (using variants for Lie and associative algebras
which are not yet in the public domain) that the
largest finite group generated by 2 elements in which
the order of every element divides 7 has order
dividing 7
^{20418}.
The program is implemented in
The program implements - a nilpotent quotient algorithm
- facilities for the computation of nilpotent groups that satisfy an Engel identity or have Engel elements as generators.
It has been used to - obtain insight into the nature of right Engel elements
- compute polycyclic presentations for infinite nilpotent Engel groups such as the free nilpotent 2-generator n-Engel group for n=4,5,6.
The implementation is written in
The program implements a finite soluble quotient algorithm. The program has been used to - compute a polycyclic presentation for B(2,6), the freest group on two generators with exponent 6.
- find small sets of sixth power relations that define certain groups of exponent six.
The program is implemented in |