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Diskr. Mat., 2018, Volume 30, Issue 1, Pages 56–65 (Mi dm1439)  

Generation of the alternating group by modular additions

F. M. Malyshev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: The paper is concerned with systems of generators of permutation groups on Cartesian products of residue rings. Each separate permutation from the system of generators is constructed on the basis of additions, is characterized by the local action, and leaves fixed the major parts of the components of the element being transformed. A criterion of 2-transitivity of the generated permutation group is given in the form of the strong connectedness of the digraph which corresponds to the system of generators and which is defined on the set of numbers of residue rings in the Cartesian product. Necessary and sufficient conditions under which this group contains an alternating group are formulated.

Keywords: permutation groups, systems of generators, local permutations.

DOI: https://doi.org/10.4213/dm1439

Full text: PDF file (452 kB)
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English version:
Discrete Mathematics and Applications, 2019, 29:5, 303–309

Bibliographic databases:

UDC: 512.542.74+512.543.1
Received: 26.06.2017

Citation: F. M. Malyshev, “Generation of the alternating group by modular additions”, Diskr. Mat., 30:1 (2018), 56–65; Discrete Math. Appl., 29:5 (2019), 303–309

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