Abstract
Given an integer \(k\ge 3\) and a group G of odd order, if there exists a 2-(v, k, 1)-design and if v is sufficiently large then there is such a design whose automorphism group has a subgroup isomorphic to G. Weaker results are obtained when |G| is even.
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Acknowledgements
I am grateful to Peter Dukes for assistance with [7], and to Jean Doyen for many helpful comments. This research was supported in part by funding from the Simons Foundation.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue: The Art of Combinatorics – A Volume in Honour of Aart Blokhuis”.
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Kantor, W.M. Automorphism subgroups for designs with \(\lambda =1\). Des. Codes Cryptogr. 90, 2145–2157 (2022). https://doi.org/10.1007/s10623-021-00936-x
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DOI: https://doi.org/10.1007/s10623-021-00936-x