Direct product of automorphism groups of digraphs

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Direct product of automorphism groups of digraphs. / Grech, Mariusz; Imrich, Wilfried; Krystek, Anna Dorota et al.
In: Ars mathematica contemporanea, Vol. 17.2019, No. 1, 01.01.2019, p. 89-101.

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Grech M, Imrich W, Krystek AD, Wojakowski ŁJ. Direct product of automorphism groups of digraphs. Ars mathematica contemporanea. 2019 Jan 1;17.2019(1):89-101. doi: 10.26493/1855-3974.1498.77b

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Grech, Mariusz ; Imrich, Wilfried ; Krystek, Anna Dorota et al. / Direct product of automorphism groups of digraphs. In: Ars mathematica contemporanea. 2019 ; Vol. 17.2019, No. 1. pp. 89-101.

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@article{2c26e00f601e4c949c7b72aad26faaa2,
title = "Direct product of automorphism groups of digraphs",
abstract = "We study the direct product of automorphism groups of digraphs, where automorphism groups are considered as permutation groups acting on the sets of vertices. By a direct product of permutation groups (A, V ) × (B, W) we mean the group (A × B, V × W) acting on the Cartesian product of the respective sets of vertices. We show that, except for the infinite family of permutation groups Sn × Sn, n ≥ 2, and four other permutation groups, namely D4 × S2, D4 × D4, S4 × S2 × S2, and C3 × C3, the direct product of automorphism groups of two digraphs is itself the automorphism group of a digraph. In the course of the proof, for each set of conditions on the groups A and B that we consider, we indicate or build a specific digraph product that, when applied to the digraphs representing A and B, yields a digraph whose automorphism group is the direct product of A and B.",
keywords = "Automorphism group, Digraph, Direct product, Permutation group",
author = "Mariusz Grech and Wilfried Imrich and Krystek, {Anna Dorota} and Wojakowski, {{\L}ukasz Jan}",
year = "2019",
month = jan,
day = "1",
doi = "10.26493/1855-3974.1498.77b",
language = "English",
volume = "17.2019",
pages = "89--101",
journal = "Ars mathematica contemporanea",
issn = "1855-3966",
publisher = "DMFA Slovenije",
number = "1",

}

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TY - JOUR

T1 - Direct product of automorphism groups of digraphs

AU - Grech, Mariusz

AU - Imrich, Wilfried

AU - Krystek, Anna Dorota

AU - Wojakowski, Łukasz Jan

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We study the direct product of automorphism groups of digraphs, where automorphism groups are considered as permutation groups acting on the sets of vertices. By a direct product of permutation groups (A, V ) × (B, W) we mean the group (A × B, V × W) acting on the Cartesian product of the respective sets of vertices. We show that, except for the infinite family of permutation groups Sn × Sn, n ≥ 2, and four other permutation groups, namely D4 × S2, D4 × D4, S4 × S2 × S2, and C3 × C3, the direct product of automorphism groups of two digraphs is itself the automorphism group of a digraph. In the course of the proof, for each set of conditions on the groups A and B that we consider, we indicate or build a specific digraph product that, when applied to the digraphs representing A and B, yields a digraph whose automorphism group is the direct product of A and B.

AB - We study the direct product of automorphism groups of digraphs, where automorphism groups are considered as permutation groups acting on the sets of vertices. By a direct product of permutation groups (A, V ) × (B, W) we mean the group (A × B, V × W) acting on the Cartesian product of the respective sets of vertices. We show that, except for the infinite family of permutation groups Sn × Sn, n ≥ 2, and four other permutation groups, namely D4 × S2, D4 × D4, S4 × S2 × S2, and C3 × C3, the direct product of automorphism groups of two digraphs is itself the automorphism group of a digraph. In the course of the proof, for each set of conditions on the groups A and B that we consider, we indicate or build a specific digraph product that, when applied to the digraphs representing A and B, yields a digraph whose automorphism group is the direct product of A and B.

KW - Automorphism group

KW - Digraph

KW - Direct product

KW - Permutation group

UR - http://www.scopus.com/inward/record.url?scp=85068332720&partnerID=8YFLogxK

U2 - 10.26493/1855-3974.1498.77b

DO - 10.26493/1855-3974.1498.77b

M3 - Article

AN - SCOPUS:85068332720

VL - 17.2019

SP - 89

EP - 101

JO - Ars mathematica contemporanea

JF - Ars mathematica contemporanea

SN - 1855-3966

IS - 1

ER -