In this paper we extend the construction of Giudici, Morgan and Zhou [8] to give the first known examples of nonregular, -closed permutation groups of rank greater than that are not the automorphism group of any digraph. We also show that this construction only gives examples for four particular primes.
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DOI : 10.5802/alco.392
Keywords: automorphism group, 2-closed, digraph
Bamberg, John 1 ; Giudici, Michael 1 ; Smith, Jacob P. 1
CC-BY 4.0
@article{ALCO_2024__7_6_1793_0,
author = {Bamberg, John and Giudici, Michael and Smith, Jacob P.},
title = {New 2-closed groups that are not automorphism groups of digraphs},
journal = {Algebraic Combinatorics},
pages = {1793--1811},
year = {2024},
publisher = {The Combinatorics Consortium},
volume = {7},
number = {6},
doi = {10.5802/alco.392},
zbl = {07966779},
language = {en},
url = {https://www.numdam.org/articles/10.5802/alco.392/}
}
TY - JOUR AU - Bamberg, John AU - Giudici, Michael AU - Smith, Jacob P. TI - New 2-closed groups that are not automorphism groups of digraphs JO - Algebraic Combinatorics PY - 2024 SP - 1793 EP - 1811 VL - 7 IS - 6 PB - The Combinatorics Consortium UR - https://www.numdam.org/articles/10.5802/alco.392/ DO - 10.5802/alco.392 LA - en ID - ALCO_2024__7_6_1793_0 ER -
%0 Journal Article %A Bamberg, John %A Giudici, Michael %A Smith, Jacob P. %T New 2-closed groups that are not automorphism groups of digraphs %J Algebraic Combinatorics %D 2024 %P 1793-1811 %V 7 %N 6 %I The Combinatorics Consortium %U https://www.numdam.org/articles/10.5802/alco.392/ %R 10.5802/alco.392 %G en %F ALCO_2024__7_6_1793_0
Bamberg, John; Giudici, Michael; Smith, Jacob P. New 2-closed groups that are not automorphism groups of digraphs. Algebraic Combinatorics, Tome 7 (2024) no. 6, pp. 1793-1811. doi: 10.5802/alco.392
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