The \(p\)–gen nature of \(M_0(V)\) (I)

• Date: 2018
• Main Author: Scott, Stuart D.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: nearring; unit; cycles (\(p\)-cycles); fixed–point–free; \(p\)–gen; 16Y30
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/746
• Journal Title: Algebra and Discrete Mathematics

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 \( V \) do...