Geodesic
The $p$-gen nature of $M_0(V)$ (I)
Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 237-268

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Let $ V $ be a finite group (not elementary two) and $ p\geq 5 $ a prime. The question as to when the nearring $ M_0(V) $ of all zero–fixing self-maps on $ V $ is generated by a unit of order $ p $ is difficult. In this paper we show $ M_0(V) $ is so generated if and only if $ V $ does not belong to one of three finite disjoint families $ {\mathcal D}^\#(1,p) $ (=$ {\mathcal D}(1,p)\cup\{\{0\}\}) $, $ {\mathcal D}(2,p) $ and $ {\mathcal D}(3,p) $ of groups, where $ {\mathcal D}(n,p) $ are those groups $ G $ (not elementary two) with $ |G|\leq np $ and $ \delta(G)>(n-1)p $ (see [1] or §.1 for the definition of $\delta(G) $).
Keywords: nearring, unit, fixed-point-free
Mots-clés : cycles ($p$-cycles), $p$-gen. 
@article{ADM_2013_15_2_a8,
     author = {S. D. Scott},
     title = {The $p$-gen nature of $M_0(V)$ {(I)}},
     journal = {Algebra and discrete mathematics},
     pages = {237--268},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a8/}
}
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S. D. Scott. The $p$-gen nature of $M_0(V)$ (I). Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 237-268. http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a8/