Christian Neumaier,
"The fraction of the bijections generating the near-ring of 0-preserving functions"
, in Archiv der Mathematik, Vol. 85, Nummer 6, Birkhäuser, Seite(n) 497-507, 2005, ISSN: 0003-889X
Original Titel:
The fraction of the bijections generating the near-ring of 0-preserving functions
Sprache des Titels:
Englisch
Original Kurzfassung:
Let $\langle G, + \rangle$ be a finite (not necessarily abelian) group. Then $M_0(G):=\{f:G \to G|f(0)=0\}$ is a near-ring, i.e., a group which is also closed under composition of functions. In Theorem 4.1 we give lower
and upper bounds for the fraction of the bijections which generate the near-ring $M_0(G)$. From these bounds we conclude the following: If $G$ has few involutions and the order of $G$ is large, then a high fraction of the bijections generate the near-ring $M_0(G)$. Also the converse holds: If a high fraction of the bijections
generate $M_0(G)$, then $G$ has few involutions
(compared to the order of $G$).
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