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Algorithms for Finding Unitals and Maximal Arcs in Projective Planes of Order 16

Stoichev, Stoicho (2007)

Serdica Journal of Computing

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakalo ff , Sofia, July, 2006.Two heuristic algorithms (M65 and M52) for finding respectively unitals and maximal arcs in projective planes of order 16 are described. The exact algorithms based on exhaustive search are impractical because of the combinatorial explosion (huge number of combinations to be checked). Algorithms M65 and M52 use unions of orbits...

Algorithms for permutability in finite groups

Adolfo Ballester-Bolinches, Enric Cosme-Llópez, Ramón Esteban-Romero (2013)

Open Mathematics

In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.

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