We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Profinite groups and centralizers of coprime automorphisms whose elements are Engel.
- Authors
Acciarri, Cristina; Sanção da Silveira, Danilo
- Abstract
Let q be a prime, n a positive integer and A an elementary abelian group of order qr with r ≥ 2 acting on a finite q'-group G. We show that if all elements in γr-1(CG(a)) are n-Engel in G for any a ∈ A#, then γr-1(G) is k-Engel for some {n, q, r}-bounded number k, and if, for some integer d such that 2d ≤ r - 1, all elements in the dth derived group of CG(a) are n-Engel in G for any a ∈ A#, then the dth derived group G(d) is k-Engel for some {n, q, r}-bounded number k. Assuming r ≥ 3, we prove that if all elements in γr-2(CG(a)) are n-Engel in CG(a) for any a ∈ A#, then γr-2(G) is k-Engel for some {n, q, r}-bounded number k, and if, for some integer d such that 2d ≤ r - 2, all elements in the dth derived group of CG(a) are n-Engel in CG(a) for any a ∈ A#, then the dth derived group G(d) is k-Engel for some {n, q, r}-bounded number k. Analogous (non-quantitative) results for profinite groups are also obtained.
- Subjects
PROFINITE groups; AUTOMORPHISMS; ENGEL curve; ABELIAN groups; FINITE groups; DERIVED categories (Mathematics)
- Publication
Journal of Group Theory, 2018, Vol 21, Issue 3, p485
- ISSN
1433-5883
- Publication type
Article
- DOI
10.1515/jgth-2018-0001