$The $p$–gen nature of $M_0(V)$ (I)$

The $p$–gen nature of $M_0(V)$ (I)

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...

Full description

Saved in:

Bibliographic Details
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
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Algebra and Discrete Mathematics

Institution

Algebra and Discrete Mathematics

id	oai:ojs.admjournal.luguniv.edu.ua:article-746
record_format	ojs
spelling	oai:ojs.admjournal.luguniv.edu.ua:article-7462018-04-26T00:55:03Z The $p$–gen nature of $M_0(V)$ (I) Scott, Stuart D. nearring, unit, cycles ($p$-cycles), fixed–point–free, $p$–gen 16Y30 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 $ {\cal D}^\#(1,p) $ (=$ {\cal D}(1,p)\cup\{\{0\}\}) $, $ {\cal D}(2,p) $ and $ {\cal D}(3,p) $ of groups, where $ {\cal 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) $). Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/746 Algebra and Discrete Mathematics; Vol 15, No 2 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/746/276 Copyright (c) 2018 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2018-04-26T00:55:03Z
collection	OJS
language	English
topic	nearring unit cycles ($p$-cycles) fixed–point–free $p$–gen 16Y30
spellingShingle	nearring unit cycles ($p$-cycles) fixed–point–free $p$–gen 16Y30 Scott, Stuart D. The $p$–gen nature of $M_0(V)$ (I)
topic_facet	nearring unit cycles ($p$-cycles) fixed–point–free $p$–gen 16Y30
format	Article
author	Scott, Stuart D.
author_facet	Scott, Stuart D.
author_sort	Scott, Stuart D.
title	The $p$–gen nature of $M_0(V)$ (I)
title_short	The $p$–gen nature of $M_0(V)$ (I)
title_full	The $p$–gen nature of $M_0(V)$ (I)
title_fullStr	The $p$–gen nature of $M_0(V)$ (I)
title_full_unstemmed	The $p$–gen nature of $M_0(V)$ (I)
title_sort	$p$–gen nature of $m_0(v)$ (i)
description	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 $ {\cal D}^\#(1,p) $ (=$ {\cal D}(1,p)\cup\{\{0\}\}) $, $ {\cal D}(2,p) $ and $ {\cal D}(3,p) $ of groups, where $ {\cal 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) $).
publisher	Lugansk National Taras Shevchenko University
publishDate	2018
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/746
work_keys_str_mv	AT scottstuartd thepgennatureofm0vi AT scottstuartd pgennatureofm0vi
first_indexed	2025-07-17T10:30:31Z
last_indexed	2025-07-17T10:30:31Z
_version_	1837889829797363712

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

Institution

Similar Items