/**************************************************************************** ** *A pq_author.h ANUPQ source Eamonn O'Brien ** *Y Copyright 1995-2001, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany *Y Copyright 1995-2001, School of Mathematical Sciences, ANU, Australia **
*/
#define PQ_VERSION "ANU p-Quotient Program Version 1.9"
/* ############################################################################### # # Australian National University p-Quotient Program # # Version 1.9 # January 2012 # # June 2001 (-v and -G options added and adapted to GAP 4) # ###############################################################################
This implementation was developed in C by
Eamonn O'Brien Department of Mathematics University of Auckland Private Bag 92019, Auckland, New Zealand
############################################################################### # # Program content # ###############################################################################
The program provides access to implementations of the following algorithms:
1. A p-quotient algorithm to compute a power-commutator presentation for a p-group. The algorithm implemented here is based on that described in Havas and Newman (1980) and papers referred to there. Another description of the algorithm appears in Vaughan-Lee (1990b). A FORTRAN implementation of this algorithm was programmed by Alford & Havas. The basic data structures of that implementation are retained.
The current implementation incorporates the following features:
a. collection from the left (see Vaughan-Lee, 1990b); Vaughan-Lee's implementation of this collection algorithm is used in the program;
b. an improved consistency algorithm (see Vaughan-Lee, 1982);
c. new exponent law enforcement and power routines;
d. closing of relations under the action of automorphisms;
e. some formula evaluation.
For details of these latter improvements, see Newman and O'Brien (1996).
2. A p-group generation algorithm to generate descriptions of p-groups. The algorithm implemented here is based on the algorithms described in Newman (1977) and O'Brien (1990). A FORTRAN implementation of this algorithm was earlier developed by Newman & O'Brien.
3. A standard presentation algorithm used to compute a canonical power-commutator presentation of a p-group. The algorithm implemented here is described in O'Brien (1994).
4. An algorithm which can be used to compute the automorphism group of a p-group. The algorithm implemented here is described in O'Brien (1995).
############################################################################### # #Access via other programs # ###############################################################################
Access to parts of this program is provided via GAP, Magma, and Quotpic.
This program is supplied as a package within GAP. The link from GAP 4 to pq is described in the ANUPQ share package manual; all of the necessary code with documentation can be found in the gap directory of this distribution.
George Havas and M.F. Newman (1980), "Application of computers to questions like those of Burnside", Burnside Groups (Bielefeld, 1977), Lecture Notes in Math. 806, pp. 211-230. Springer-Verlag.
M.F. Newman (1977), "Determination of groups of prime-power order", Group Theory (Canberra, 1975). Lecture Notes in Math. 573, pp. 73-84. Springer-Verlag.
M.F. Newman and E.A. O'Brien (1996), "Application of computers to questions like those of Burnside II", Internat. J. Algebra Comput.
E.A. O'Brien (1990), "The p-group generation algorithm", J. Symbolic Comput. 9, 677-698.
E.A. O'Brien (1994), ``Isomorphism testing for p-groups", J. Symbolic Comput. 17, 133-147.
E.A. O'Brien (1995), ``Computing automorphism groups of p-groups", Computational Algebra and Number Theory, (Sydney, 1992), pp. 83--90. Kluwer Academic Publishers, Dordrecht.
M.R. Vaughan-Lee (1982), "An Aspect of the Nilpotent Quotient Algorithm", Computational Group Theory (Durham, 1982), pp. 76-83. Academic Press.
Michael Vaughan-Lee (1990a), The Restricted Burnside Problem, London Mathematical Society monographs (New Ser.) #5. Clarendon Press, New York, Oxford.
M.R. Vaughan-Lee (1990b), "Collection from the left", J. Symbolic Comput. 9, 725-733.
*/
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