## Computing projectors, injectors, residuals and radicals of finite soluble groups.(English)Zbl 0990.20008

The author presents algorithms for computing subgroups of a group related to Schunck and Fitting classes. They can be considered a generalization of methods of B. Eick and C. R. B. Wright for formations [J. Symb. Comput. 33, No. 2, 129-143 (2002; Zbl 0995.20004)]. As an application, the author obtains a method for computing normal subgroups for a solvable group, which improves on the algorithm of the reviewer [Proceedings of the 1998 international symposium on symbolic and algebraic computation, 194-198 (1998; Zbl 0943.20005)].

### MSC:

 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, $$\pi$$-length, ranks 68W30 Symbolic computation and algebraic computation 20-04 Software, source code, etc. for problems pertaining to group theory

### Keywords:

solvable groups; Schunck classes; Fitting classes; algorithms

### Citations:

Zbl 0943.20005; Zbl 0995.20004

CRISP; GAP
Full Text:

### References:

 [1] Butler, G., Fundamental algorithms for permutation groups, (1991), Springer Berlin · Zbl 0785.20001 [2] Celler, F.; Neubüser, J.; Wright, C.R.B., Some remarks on the computation of complements and normalizers in soluble groups, Acta appl. math., 21, 57-76, (1990) · Zbl 0719.20010 [3] Doerk, K.; Hawkes, T., Finite soluble groups, (1992), de Gruyter Berlin · Zbl 0753.20001 [4] Eick, B.; Wright, C.R.B., Computing subgroups by exhibition in finite solvable groups, J. symb. comput. to appear., (2000) [5] B. Eick, C. R. B. Wright [6] The GAP Group [7] B. Höfling [8] Holt, D.F.; Rees, S., Testing modules for irreducibility, J. austral. math. soc. ser. A, 57, 1-16, (1994) · Zbl 0833.20021 [9] A. Hulpke, Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation, 1998, Association for Computing Machinery [10] Laue, R.; Neubüser, J.; Schoenwaelder, U., Algorithms for finite soluble groups and the SOGOS system, () · Zbl 0547.20012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.