A pastiche on embeddings into simple groups (following P. E. Schupp)
| dc.creator | Sunic, Zoran | |
| dc.date | 2007-11-03 | |
| dc.date | 2008-02-07 | |
| dc.date.accessioned | 2026-07-07T09:18:56Z | |
| dc.date.available | 2026-07-07T09:18:56Z | |
| dc.description | Let lambda be an infinite cardinal number and let C = {H_i| i in I} be a family of nontrivial groups. Assume that |I|<=lambda, |H_i|<= lambda, for i in I, and at least one member of C achieves the cardinality lambda. We show that there exists a simple group S of cardinality lambda that contains an isomorphic copy of each member of C and, for all H_i, H_j in C with |H_j|=lambda, is generated by the copies of H_i and H_j in S. This generalizes a result of Paul E. Schupp (moreover, our proof follows the same approach based on small cancelation). In the countable case, we partially recover a much deeper embedding result of Alexander Yu. Ol'shanskii. | |
| dc.description | added details in the definition of C'(1/6) over free products | |
| dc.identifier | https://arxiv.org/abs/0711.0476 | |
| dc.identifier | http://arxiv.org/abs/0711.0476 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154209 | |
| dc.subject | Group Theory | |
| dc.subject | 20F06, 20E32 | |
| dc.title | A pastiche on embeddings into simple groups (following P. E. Schupp) | |
| dc.type | text |