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Moufang sets generated by translations in unitals

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Organization
Abstract
We consider unitals of order q with two points which are centers of translation groups of order q. The group G generated by these translations induces a Moufang set on the block joining the two points. We show that G is either SL ( 2 , F q ) (as in all classical unitals and also in some nonclassical examples), or PSL ( 2 , F q ), or a Suzuki, or a Ree group. Moreover, G is semiregular outside the special block.
Keywords
TRANSITIVE PERMUTATION-GROUPS, GENERALIZED QUADRANGLES, MULTIPLICATORS, FIXES, automorphism, design, Moufang set, Ree group, Suzuki group, translation, two-transitive group, unital, unitary group

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MLA
Grundhoefer, Theo, et al. “Moufang Sets Generated by Translations in Unitals.” JOURNAL OF COMBINATORIAL DESIGNS, vol. 30, no. 2, Wiley, 2022, pp. 91–104, doi:10.1002/jcd.21813.
APA
Grundhoefer, T., Stroppel, M. J., & Van Maldeghem, H. (2022). Moufang sets generated by translations in unitals. JOURNAL OF COMBINATORIAL DESIGNS, 30(2), 91–104. https://doi.org/10.1002/jcd.21813
Chicago author-date
Grundhoefer, Theo, Markus J. Stroppel, and Hendrik Van Maldeghem. 2022. “Moufang Sets Generated by Translations in Unitals.” JOURNAL OF COMBINATORIAL DESIGNS 30 (2): 91–104. https://doi.org/10.1002/jcd.21813.
Chicago author-date (all authors)
Grundhoefer, Theo, Markus J. Stroppel, and Hendrik Van Maldeghem. 2022. “Moufang Sets Generated by Translations in Unitals.” JOURNAL OF COMBINATORIAL DESIGNS 30 (2): 91–104. doi:10.1002/jcd.21813.
Vancouver
1.
Grundhoefer T, Stroppel MJ, Van Maldeghem H. Moufang sets generated by translations in unitals. JOURNAL OF COMBINATORIAL DESIGNS. 2022;30(2):91–104.
IEEE
[1]
T. Grundhoefer, M. J. Stroppel, and H. Van Maldeghem, “Moufang sets generated by translations in unitals,” JOURNAL OF COMBINATORIAL DESIGNS, vol. 30, no. 2, pp. 91–104, 2022.
@article{8755218,
  abstract     = {{We consider unitals of order q with two points which are centers of translation groups of order q. The group G generated by these translations induces a Moufang set on the block joining the two points. We show that G is either SL ( 2 , F q ) (as in all classical unitals and also in some nonclassical examples), or PSL ( 2 , F q ), or a Suzuki, or a Ree group. Moreover, G is semiregular outside the special block.}},
  author       = {{Grundhoefer, Theo and Stroppel, Markus J. and Van Maldeghem, Hendrik}},
  issn         = {{1063-8539}},
  journal      = {{JOURNAL OF COMBINATORIAL DESIGNS}},
  keywords     = {{TRANSITIVE PERMUTATION-GROUPS,GENERALIZED QUADRANGLES,MULTIPLICATORS,FIXES,automorphism,design,Moufang set,Ree group,Suzuki group,translation,two-transitive group,unital,unitary group}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{91--104}},
  publisher    = {{Wiley}},
  title        = {{Moufang sets generated by translations in unitals}},
  url          = {{http://dx.doi.org/10.1002/jcd.21813}},
  volume       = {{30}},
  year         = {{2022}},
}

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