Nilpotent Singer Groups
Keyword(s):
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.
1990 ◽
Vol 48
(1)
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pp. 156-170
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Keyword(s):
1978 ◽
Vol 25
(1)
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pp. 19-24
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Keyword(s):
Keyword(s):
1957 ◽
Vol 9
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pp. 378-388
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2018 ◽
Vol 17
(04)
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pp. 1850065