The automorphism tower of a centerless group (mostly) without choice
| dc.creator | Kaplan, Itay | |
| dc.creator | Shelah, Saharon | |
| dc.date | 2006-06-09 | |
| dc.date.accessioned | 2026-07-07T07:17:08Z | |
| dc.date.available | 2026-07-07T07:17:08Z | |
| dc.description | For a centerless group G, we can define its automorphism tower. We define G^{alpha} : G^0=G, G^{alpha +1}=Aut(G^alpha) and for limit ordinals G^delta=bigcup_{alpha < delta}G^alpha . Let tau_G be the ordinal when the sequence stabilizes. Thomas' celebrated theorem says tau_G<2^{|G|})^{+} and more. If we consider Thomas' proof too set theoretical, we have here a shorter proof with little set theory. However, set theoretically we get a parallel theorem without the axiom of choice. We attach to every element in G^alpha, the alpha-th member of the automorphism tower of G, a unique quantifier free type over G (whish is a set of words from G*< x>). This situation is generalized by defining ``(G,A) is a special pair''. | |
| dc.identifier | https://arxiv.org/abs/math/0606216 | |
| dc.identifier | http://arxiv.org/abs/math/0606216 | |
| dc.identifier | Arch. Math. Logic 48 No. 8 (2009) 799--815 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113832 | |
| dc.subject | Logic | |
| dc.subject | Group Theory | |
| dc.title | The automorphism tower of a centerless group (mostly) without choice | |
| dc.type | text |