Geodesic
Nilpotent Singer groups.
The electronic journal of combinatorics, Tome 13 (2006)
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Let $N$ be a nilpotent group normal in a group $G$. Suppose that $G$ acts transitively upon the points of a finite non-Desarguesian projective plane ${\cal P}$. We prove that, if ${\cal P}$ has square order, then $N$ must act semi-regularly on ${\cal P}$. In addition we prove that if a finite non-Desarguesian projective plane ${\cal P}$ admits more than one nilpotent group which is regular on the points of ${\cal P}$ then ${\cal P}$ has non-square order and the automorphism group of ${\cal P}$ has odd order.
DOI : 10.37236/1120
Classification : 20B25, 05B25, 51A35
Mots-clés : nilpotent normal subgroups, finite non-Desarguesian projective planes, automorphism groups 
@article{10_37236_1120,
     author = {Nick Gill},
     title = {Nilpotent {Singer} groups.},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1120},
     zbl = {1118.20003},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1120/}
}
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DO  - 10.37236/1120
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Nick Gill. Nilpotent Singer groups.. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1120

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