The Format GAP4 Package

The GAP4 package Format by Bettina Eick and Charles R.B. Wright provides programs for computing with formations of finite solvable groups and with various formation-theoretic subgroups. In addition to tools for constructing and combining formations, the package contains functions to compute F-residual subgroups and to construct F-normalizers and F-covering subgroups determined by locally defined formations. System normalizers and Carter subgroups are available as special cases. The F-normalizer functions also apply to the computation of complements. The corresponding algorithms, together with applications and a complexity analysis, are described in a related article.

The package permits the computation of formation-theoretic subgroups not only for a number of classical formations, such as nilpotent, supersolvable and p-length 1 groups, but also for other formations that the user may define, and it allows computation with classes of finite solvable groups defined by normal subgroup functions (see Doerk and Hawkes, Finite Soluble Groups, pages 395ff). Attention may be restricted to the subgroups of a single group, a feature that has applications in the computation of complements to elementary abelian normal subgroups in finite solvable groups. An example of such an application is described in the Format manual.

The package itself is available here and as part of the GAP distribution.

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Last modified 11-8-11 by CRBW