# Conjugates for Finding the Automorphism Group and Isomorphism of Design Resolutions

• Volume: 10, Issue: 1, page 079-092
• ISSN: 1312-6555

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## Abstract

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Consider a combinatorial design D with a full automorphism group G D. The automorphism group G of a design resolution R is a subgroup of G D. This subgroup maps each parallel class of R into a parallel class of R. Two resolutions R 1 and R 2 of D are isomorphic if some automorphism from G D maps each parallel class of R 1 to a parallel class of R 2. If G D is very big, the computation of the automorphism group of a resolution and the check for isomorphism of two resolutions might be difficult. Such problems often arise when resolutions of geometric designs (the designs of the points and t-dimensional subspaces of projective or affine spaces) are considered. For resolutions with given automorphisms these problems can be solved by using some of the conjugates of the predefined automorphisms. The method is explained in the present paper and an algorithm for construction of the necessary conjugates is presented. ACM Computing Classification System (1998): F.2.1, G.1.10, G.2.1.

## How to cite

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Topalova, Svetlana. "Conjugates for Finding the Automorphism Group and Isomorphism of Design Resolutions." Serdica Journal of Computing 10.1 (2016): 079-092. <http://eudml.org/doc/289537>.

@article{Topalova2016,
abstract = {Consider a combinatorial design D with a full automorphism group G D. The automorphism group G of a design resolution R is a subgroup of G D. This subgroup maps each parallel class of R into a parallel class of R. Two resolutions R 1 and R 2 of D are isomorphic if some automorphism from G D maps each parallel class of R 1 to a parallel class of R 2. If G D is very big, the computation of the automorphism group of a resolution and the check for isomorphism of two resolutions might be difficult. Such problems often arise when resolutions of geometric designs (the designs of the points and t-dimensional subspaces of projective or affine spaces) are considered. For resolutions with given automorphisms these problems can be solved by using some of the conjugates of the predefined automorphisms. The method is explained in the present paper and an algorithm for construction of the necessary conjugates is presented. ACM Computing Classification System (1998): F.2.1, G.1.10, G.2.1.},
author = {Topalova, Svetlana},
journal = {Serdica Journal of Computing},
keywords = {Conjugates; Design Resolutions; Parallelisms; Automorphism Group},
language = {eng},
number = {1},
pages = {079-092},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Conjugates for Finding the Automorphism Group and Isomorphism of Design Resolutions},
url = {http://eudml.org/doc/289537},
volume = {10},
year = {2016},
}

TY - JOUR
AU - Topalova, Svetlana
TI - Conjugates for Finding the Automorphism Group and Isomorphism of Design Resolutions
JO - Serdica Journal of Computing
PY - 2016
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 10
IS - 1
SP - 079
EP - 092
AB - Consider a combinatorial design D with a full automorphism group G D. The automorphism group G of a design resolution R is a subgroup of G D. This subgroup maps each parallel class of R into a parallel class of R. Two resolutions R 1 and R 2 of D are isomorphic if some automorphism from G D maps each parallel class of R 1 to a parallel class of R 2. If G D is very big, the computation of the automorphism group of a resolution and the check for isomorphism of two resolutions might be difficult. Such problems often arise when resolutions of geometric designs (the designs of the points and t-dimensional subspaces of projective or affine spaces) are considered. For resolutions with given automorphisms these problems can be solved by using some of the conjugates of the predefined automorphisms. The method is explained in the present paper and an algorithm for construction of the necessary conjugates is presented. ACM Computing Classification System (1998): F.2.1, G.1.10, G.2.1.
LA - eng
KW - Conjugates; Design Resolutions; Parallelisms; Automorphism Group
UR - http://eudml.org/doc/289537
ER -

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