Let M be a countable recursively saturated model of PA and H an open subgroup of G = Aut(M). We prove that I ( H ) = sup{b E M : (3f E G \ H )
Computing Subgroups Invariant Under a Set of Automorphisms
β Scribed by A. Hulpke
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 442 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0747-7171
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β¦ Synopsis
This article describes an algorithm for computing up to conjugacy all subgroups of a finite solvable group that are invariant under a set of automorphisms. It constructs the subgroups stepping down along a normal chain with elementary abelian factors.
π SIMILAR VOLUMES
Let F be a finitely generated free group, and let n denote its rank. A subgroup H of F is said to be automorphism-fixed, or auto-fixed for short, if there exists a set S of automorphisms of F such that H is precisely the set of elements fixed by every element of S; similarly, H is 1-auto-fixed if th
A new method for computing the conjugacy classes of subgroups of a finite group is described.
## Abstract We show that if __M__ is a countable recursively saturated model of True Arithmetic, then __G__ = Aut(__M__) has nonmaximal open subgroups with unique extension to a maximal subgroup of Aut(__M__). Mathematics Subject Classification: 03C62, 03C50.
Continuing the earlier research in [14] we give some more information about nonmaximal open subgroups of G = Aut(M) with unique maximal extension, where M is a countable recursively saturated model of True Arithmetic.