The following materials are available in the RESEARCH subdirectory:
This paper describes practical algorithms for computing residual subgroups, F-normalizers, and F-covering subgroups for finite soluble groups and saturated formations F. The algorithms, which do not use chief factors, depend on modifying generating sequences to exhibit the desired subgroups. For commonly considered formations, the algorithms run in time polynomial in the composition length of the group and the largest prime divisor of its order.
This article has appeared in the
The GAP4 package FORMAT contains programs that carry out the algorithms in the paper.
A description of the Format package, with links to the package's manual in various forms.
A tarball and a bz2 archive of the package itself.
Some Algorithms for Nilpotent Permutation Groups, with E. M. Luks and F. Rákóczi.
Let G, H and E be subgroups of a finite nilpotent permutation group of degree n. We describe the theory and implementation of an algorithm to compute the normalizer of H in G in time polynomial in n, and we give a modified algorithm to determine whether H and E are conjugate under G and, if so, to find a conjugating element of G. Other algorithms produce the intersection of G and H and the centralizer of H in G.
The underlying method uses the imprimitivity structure of <G,H> and an associated canonical chief series to reduce computation to linear operations. Implementations in GAP and Magma are practical for degrees large enough to present difficulties for general-purpose methods.
This article has appeared in the Journal for Symbolic Computation (Vol. 23, pp 335–354, 1997). It is available here as a dvi file LRW.dvi (102K) and as a PostScript file LRW.ps (250K).
An Internal Approach to Covering Groups
This note gives an account of generalized normalizers and covering groups. The extended notions are used in an iterative scheme that produces covering groups from normalizers, and the rate of convergence of the methods is discussed.
This paper describes analogues to internally induced formations that are defined entirely within a given finite solvable group. The methods are used to construct complements to normat subgroups and to determine when all such complements are conjugate. These methods are implemented in the FORMAT GAP package; see the FORMAT manual for details and an example.
Last modified 4/1/19 by CRBW