JEDNOSTKA NAUKOWA KATEGORII A+

Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

Colloquium Mathematicum

Artykuły w formacie PDF dostępne są dla subskrybentów, którzy zapłacili za dostęp online, po podpisaniu licencji Licencja użytkownika instytucjonalnego. Czasopisma do 2009 są ogólnodostępne (bezpłatnie).

Finite-finitary, polycyclic-finitary and Chernikov-finitary automorphism groups

Tom 138 / 2015

Colloquium Mathematicum 138 (2015), 1-22 MSC: 20F28, 20E36. DOI: 10.4064/cm138-1-1

Streszczenie

If X is a property or a class of groups, an automorphism $\phi$ of a group $G$ is X-finitary if there is a normal subgroup $N$ of $G$ centralized by $\phi$ such that $G/N$ is an X-group. Groups of such automorphisms for $G$ a module over some ring have been very extensively studied over many years. However, for groups in general almost nothing seems to have been done. In 2009 V. V. Belyaev and D. A. Shved considered the general case for X the class of finite groups. Here we look further at the finite case but our main results concern the cases where X is either the class of polycyclic-by-finite groups or the class of Chernikov groups. The latter presents a new perspective on some work of Ya. D. Polovitskiĭ in the 1960s, which seems to have been at least partially overlooked in recent years. Our polycyclic cases present a different view of work of S. Franciosi, F. de Giovanni and M. J. Tomkinson from 1990. We describe the polycyclic cases in terms of matrix groups over the integers, and the Chernikov case in terms of matrix groups over the complex numbers.

Autorzy

• B. A. F. WehrfritzSchool of Mathematical Sciences
Queen Mary University of London
London E1 4NS, England
e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek