Abstract
A subgroup of any group is called conjugately dense if it has nonempty intersection with each class of conjugate elements of the group. The aim of this paper is to prove the following. Let K be a locally finite field and H be an irreducible conjugately dense subgroup of the intermediate group SL 3(K) ≤ G ≤ GL3(K); then H = G. This result confirms part of P. Neumann's conjecture from problem 6.38 in "Kourovka Notebook" for the group GL3(K) over locally finite field K.
| Original language | English |
|---|---|
| Pages (from-to) | 1273-1280 |
| Number of pages | 8 |
| Journal | International Journal of Algebra and Computation |
| Volume | 15 |
| Issue number | 5-6 |
| DOIs | |
| Publication status | Published - 1 Oct 2005 |
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Keywords
- Conjugacy class
- Irreducible and conjugately dense subgroup
- Special and general linear group
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Conjugately dense subgroups of 3-dimensional linear groups over locally finite field. / Zyubin, S. A.
In: International Journal of Algebra and Computation, Vol. 15, No. 5-6, 01.10.2005, p. 1273-1280.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Conjugately dense subgroups of 3-dimensional linear groups over locally finite field
AU - Zyubin, S. A.
PY - 2005/10/1
Y1 - 2005/10/1
N2 - A subgroup of any group is called conjugately dense if it has nonempty intersection with each class of conjugate elements of the group. The aim of this paper is to prove the following. Let K be a locally finite field and H be an irreducible conjugately dense subgroup of the intermediate group SL 3(K) ≤ G ≤ GL3(K); then H = G. This result confirms part of P. Neumann's conjecture from problem 6.38 in "Kourovka Notebook" for the group GL3(K) over locally finite field K.
AB - A subgroup of any group is called conjugately dense if it has nonempty intersection with each class of conjugate elements of the group. The aim of this paper is to prove the following. Let K be a locally finite field and H be an irreducible conjugately dense subgroup of the intermediate group SL 3(K) ≤ G ≤ GL3(K); then H = G. This result confirms part of P. Neumann's conjecture from problem 6.38 in "Kourovka Notebook" for the group GL3(K) over locally finite field K.
KW - Conjugacy class
KW - Irreducible and conjugately dense subgroup
KW - Special and general linear group
UR - http://www.scopus.com/inward/record.url?scp=30344477618&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=30344477618&partnerID=8YFLogxK
U2 - 10.1142/S0218196705002608
DO - 10.1142/S0218196705002608
M3 - Article
VL - 15
SP - 1273
EP - 1280
JO - International Journal of Algebra and Computation
JF - International Journal of Algebra and Computation
SN - 0218-1967
IS - 5-6
ER -