| Title:
|
On groups of similitudes in associative rings (English) |
| Author:
|
Bashkirov, Evgenii L. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
525-531 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be an associative ring with 1 and $R^{\times}$ the multiplicative group of invertible elements of $R$. In the paper, subgroups of $R^{\times}$ which may be regarded as analogues of the similitude group of a non-degenerate sesquilinear reflexive form and of the isometry group of such a form are defined in an abstract way. The main result states that a unipotent abstractly defined similitude must belong to the corresponding abstractly defined isometry group. (English) |
| Keyword:
|
associative rings |
| Keyword:
|
unipotent elements |
| MSC:
|
16U60 |
| MSC:
|
20H25 |
| idZBL:
|
Zbl 1192.16034 |
| idMR:
|
MR2493935 |
| . |
| Date available:
|
2009-05-05T17:12:56Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119743 |
| . |
| Reference:
|
[1] Bashkirov E.L.: Linear groups that contain a root subgroup.Siberian Math. J. 37 (1996), 5 754-759. MR 1440380, 10.1007/BF02106733 |
| Reference:
|
[2] Bashkirov E.L.: Irreducible linear groups of degree four over a quaternion division algebra that contain a subgroup diag$(T_{3}(K,\Phi_{0}),1)$.J. Algebra 287 (2005), 2 319-350. Zbl 1088.20030, MR 2134148, 10.1016/j.jalgebra.2004.09.006 |
| Reference:
|
[3] Bashkirov E.L.: Irreducible linear groups of degree four over a quaternion division algebra that contain a root subgroup.Comm. Algebra 34 (2006), 6 1931-1948. Zbl 1110.20038, MR 2235072, 10.1080/00927870500454802 |
| Reference:
|
[4] Bashkirov E.L.: Completely reducible linear groups over a quaternion division algebra that contain a root subgroup.Comm. Algebra 35 (2007), 3 1019-1054. Zbl 1118.20049, MR 2305248, 10.1080/00927870601074798 |
| Reference:
|
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| Reference:
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| Reference:
|
[7] Dye R.H.: Maximal subgroups of ${GL}_{2n}(K)$, ${SL}_{2n}(K)$, ${PGL}_{2n}(K)$ and ${PSL}_{2n}(K)$ associated with symplectic polarities.J. Algebra 66 (1980), 1 1-11. Zbl 0444.20036, MR 0591244, 10.1016/0021-8693(80)90110-6 |
| Reference:
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[8] King O.H.: On subgroups of the special linear group containing the special orthogonal group.J. Algebra 96 (1985), 1 178-193. Zbl 0572.20028, MR 0808847, 10.1016/0021-8693(85)90045-6 |
| Reference:
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| Reference:
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| . |
