On recognition of direct powers of finite simple linear groups by spectrum
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917685474885632 |
|---|---|
| author | Yang, N. Gorshkov, I. B. Staroletov, A. M. Vasil'ev, A. V. |
| author_facet | Yang, N. Gorshkov, I. B. Staroletov, A. M. Vasil'ev, A. V. |
| contents | The spectrum of a finite group is the set of its element orders. We give an affirmative answer to Problem 20.58(a) from the Kourovka Notebook proving that for every positive integer $k$, the $k$-th direct power of the simple linear group $L_{n}(2)$ is uniquely determined by its spectrum in the class of finite groups provided $n$ is a power of $2$ greater than or equal to $56k^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13759 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On recognition of direct powers of finite simple linear groups by spectrum Yang, N. Gorshkov, I. B. Staroletov, A. M. Vasil'ev, A. V. Group Theory 20D06 The spectrum of a finite group is the set of its element orders. We give an affirmative answer to Problem 20.58(a) from the Kourovka Notebook proving that for every positive integer $k$, the $k$-th direct power of the simple linear group $L_{n}(2)$ is uniquely determined by its spectrum in the class of finite groups provided $n$ is a power of $2$ greater than or equal to $56k^2$. |
| title | On recognition of direct powers of finite simple linear groups by spectrum |
| topic | Group Theory 20D06 |
| url | https://arxiv.org/abs/2210.13759 |