| Title:
|
Infinite dimensional linear groups with a large family of $G$-invariant subspaces (English) |
| Author:
|
Kurdachenko, L. A. |
| Author:
|
Sadovnichenko, A. V. |
| Author:
|
Subbotin, I. Ya. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
551-558 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $F$ be a field, $A$ be a vector space over $F$, $\operatorname{GL}(F,A)$ be the group of all automorphisms of the vector space $A$. A subspace $B$ is called almost $G$-invariant, if $\dim _{F}(B/\operatorname{Core}_{G}(B))$ is finite. In the current article, we begin the study of those subgroups $G$ of $\operatorname{GL}(F,A)$ for which every subspace of $A$ is almost $G$-invariant. More precisely, we consider the case when $G$ is a periodic group. We prove that in this case $A$ includes a $G$-invariant subspace $B$ of finite codimension whose subspaces are $G$-invariant. (English) |
| Keyword:
|
vector space |
| Keyword:
|
linear groups |
| Keyword:
|
periodic groups |
| Keyword:
|
soluble groups |
| Keyword:
|
invariant subspaces |
| MSC:
|
15A03 |
| MSC:
|
20F16 |
| MSC:
|
20F29 |
| idZBL:
|
Zbl 1224.15002 |
| idMR:
|
MR2858259 |
| . |
| Date available:
|
2010-11-30T16:15:01Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140835 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
