$On some linear groups, having a big family of $G$-invariant subspaces$

On some linear groups, having a big family of $G$-invariant subspaces

Let $F$ be a field, $A$ a vector space over $F$, $GL(F, A)$ be the group of all automorphisms of the vector space $A$. If $B$ is a subspace of $A$, then denote by $BFG$ the $G$-invariant subspace, generated by $B$. A subspace $B$ is called nearly $G$-invariant, if \(dim_F(BFG...

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Дата:	2018
Автори:	Kurdachenko, L. A., Sadovnichenko, A. V.
Формат:	Стаття
Мова:	English
Опубліковано:	Lugansk National Taras Shevchenko University 2018
Теми:	Vector space linear group module $G$-invariant subspace nearly $G$-invariant subspace 15A03 20F16 20F29
Онлайн доступ:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1158
Теги:	Додати тег Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	oai:ojs.admjournal.luguniv.edu.ua:article-1158
record_format	ojs
spelling	oai:ojs.admjournal.luguniv.edu.ua:article-11582018-05-16T05:04:06Z On some linear groups, having a big family of $G$-invariant subspaces Kurdachenko, L. A. Sadovnichenko, A. V. Vector space, linear group, module, $G$-invariant subspace, nearly $G$-invariant subspace 15A03, 20F16, 20F29 Let $F$ be a field, $A$ a vector space over $F$, $GL(F, A)$ be the group of all automorphisms of the vector space $A$. If $B$ is a subspace of $A$, then denote by $BFG$ the $G$-invariant subspace, generated by $B$. A subspace $B$ is called nearly $G$-invariant, if $dim_F(BFG/B)$ is finite. In this paper we described the situation when every subspace of $A$ is nearly $G$-invariant. Lugansk National Taras Shevchenko University 2018-05-16 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1158 Algebra and Discrete Mathematics; Vol 16, No 2 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1158/650 Copyright (c) 2018 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
collection	OJS
language	English
topic	Vector space linear group module $G$-invariant subspace nearly $G$-invariant subspace 15A03 20F16 20F29
spellingShingle	Vector space linear group module $G$-invariant subspace nearly $G$-invariant subspace 15A03 20F16 20F29 Kurdachenko, L. A. Sadovnichenko, A. V. On some linear groups, having a big family of $G$-invariant subspaces
topic_facet	Vector space linear group module $G$-invariant subspace nearly $G$-invariant subspace 15A03 20F16 20F29
format	Article
author	Kurdachenko, L. A. Sadovnichenko, A. V.
author_facet	Kurdachenko, L. A. Sadovnichenko, A. V.
author_sort	Kurdachenko, L. A.
title	On some linear groups, having a big family of $G$-invariant subspaces
title_short	On some linear groups, having a big family of $G$-invariant subspaces
title_full	On some linear groups, having a big family of $G$-invariant subspaces
title_fullStr	On some linear groups, having a big family of $G$-invariant subspaces
title_full_unstemmed	On some linear groups, having a big family of $G$-invariant subspaces
title_sort	on some linear groups, having a big family of $g$-invariant subspaces
description	Let $F$ be a field, $A$ a vector space over $F$, $GL(F, A)$ be the group of all automorphisms of the vector space $A$. If $B$ is a subspace of $A$, then denote by $BFG$ the $G$-invariant subspace, generated by $B$. A subspace $B$ is called nearly $G$-invariant, if $dim_F(BFG/B)$ is finite. In this paper we described the situation when every subspace of $A$ is nearly $G$-invariant.
publisher	Lugansk National Taras Shevchenko University
publishDate	2018
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1158
work_keys_str_mv	AT kurdachenkola onsomelineargroupshavingabigfamilyofginvariantsubspaces AT sadovnichenkoav onsomelineargroupshavingabigfamilyofginvariantsubspaces
first_indexed	2024-04-12T06:26:01Z
last_indexed	2024-04-12T06:26:01Z
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On some linear groups, having a big family of \(G\)-invariant subspaces

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