On Socle and Semisimple Groups
We prove a theorem that gives a large array of new counterexamples to the known Baer (1949) and S. Chernikov (1959) problems related to socle groups. All these counterexamples are semisimple groups. We also establish many new properties of locally subinvariant semisimple subgroups. In particular, us...
Saved in:
| Date: | 2002 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2002
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4123 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510259659931648 |
|---|---|
| author | Chernikov, N. S. Черников, Н. С. Черников, Н. С. |
| author_facet | Chernikov, N. S. Черников, Н. С. Черников, Н. С. |
| author_sort | Chernikov, N. S. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:22:38Z |
| description | We prove a theorem that gives a large array of new counterexamples to the known Baer (1949) and S. Chernikov (1959) problems related to socle groups. All these counterexamples are semisimple groups. We also establish many new properties of locally subinvariant semisimple subgroups. In particular, using these properties, we prove that all almost locally solvable M′-groups are Chernikov groups. |
| first_indexed | 2026-03-24T02:54:10Z |
| format | Article |
| fulltext |
0126
0127
0128
0129
0130
0131
0132
0133
0134
0135
0136
0137
0138
0139
0140
|
| id | umjimathkievua-article-4123 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:54:10Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/9d/f781405ad12d4d50abc02e47ba98a29d.pdf |
| spelling | umjimathkievua-article-41232020-03-18T20:22:38Z On Socle and Semisimple Groups О цокольных и полупростых группах Chernikov, N. S. Черников, Н. С. Черников, Н. С. We prove a theorem that gives a large array of new counterexamples to the known Baer (1949) and S. Chernikov (1959) problems related to socle groups. All these counterexamples are semisimple groups. We also establish many new properties of locally subinvariant semisimple subgroups. In particular, using these properties, we prove that all almost locally solvable M′-groups are Chernikov groups. Доведемо теорему, яка дає великий масив иових коптрприкладів до відомих проблем Р. Бера (1949 р.) та С. М. Черпікова (1959 p.), що пов'язані із цокольними групами. Всі коїп рприклади є папівпростими групами. Встановлено також багато иових властивостей локально субінва-ріаптпих папівпростих підгруп. На підставі цих властивостей, зокрема, доведено, що всі майже локально розв'язні M′-групи є черпіковськими. Institute of Mathematics, NAS of Ukraine 2002-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4123 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 6 (2002); 866-880 Український математичний журнал; Том 54 № 6 (2002); 866-880 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4123/4955 https://umj.imath.kiev.ua/index.php/umj/article/view/4123/4956 Copyright (c) 2002 Chernikov N. S. |
| spellingShingle | Chernikov, N. S. Черников, Н. С. Черников, Н. С. On Socle and Semisimple Groups |
| title | On Socle and Semisimple Groups |
| title_alt | О цокольных и полупростых группах |
| title_full | On Socle and Semisimple Groups |
| title_fullStr | On Socle and Semisimple Groups |
| title_full_unstemmed | On Socle and Semisimple Groups |
| title_short | On Socle and Semisimple Groups |
| title_sort | on socle and semisimple groups |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4123 |
| work_keys_str_mv | AT chernikovns onsocleandsemisimplegroups AT černikovns onsocleandsemisimplegroups AT černikovns onsocleandsemisimplegroups AT chernikovns ocokolʹnyhipoluprostyhgruppah AT černikovns ocokolʹnyhipoluprostyhgruppah AT černikovns ocokolʹnyhipoluprostyhgruppah |