Direct product of automorphism groups of digraphs
Research output: Contribution to journal › Article › Research › peer-review
Standard
In: Ars mathematica contemporanea, Vol. 17.2019, No. 1, 01.01.2019, p. 89-101.
Research output: Contribution to journal › Article › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex - Download
}
RIS (suitable for import to EndNote) - Download
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 -
