PreprintCC BY-NC-ND 4.0arXiv
The group class SJ is not countably recognizable
Abstract
A group is an {\it SJ-group} if it admits a general abelian series all of whose terms are subnormal of finite defect in the whole group. We construct a group G which is not an~\hbox{SJ-group}, although every countable subgroup of G is an SJ-group.
Related
- Monogenicity and 2-torsion in the class group of number fields of odd degree
- A Faithful Action of the Mapping Class Group Mod(Sg) on the (2gā1)-Sphere
- Generating the twist subgroup of the level $2$ mapping class group of a non-orientable closed surface
- Lie groups are countably representable
- An explicit section of the Laudenbach-type exact sequence of the big mapping class group of MĪ
BibTeX
@misc{brescia2026group,
title = {{The group class SJ is not countably recognizable}},
author = {M. Brescia and B. G. Di Siena and E. Ingrosso and M. Trombetti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05415},
eprint = {2610.05415},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05415},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The group class SJ is not countably recognizable
AU - M. Brescia
AU - B. G. Di Siena
AU - E. Ingrosso
AU - M. Trombetti
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05415
UR - https://arxiv.org/abs/2610.05415
AB - A group is an {\it SJ-group} if it admits a general abelian series all of whose terms are subnormal of finite defect in the whole group. We construct a group G which is not an~\hbox{SJ-group}, although every countable subgroup of G is an SJ-group.
ER -