Affordable Access

Absolute irreducibility for finitary linear groups

Authors
Publication Date
Disciplines
  • Law
  • Mathematics

Abstract

Absolute irreducibility for finitary linear groups RENDICONTI del SEMINARIO MATEMATICO della UNIVERSITÀ DI PADOVA FELIX LEINEN Absolute irreducibility for finitary linear groups Rendiconti del Seminario Matematico della Università di Padova, tome 92 (1994), p. 59-61. <http://www.numdam.org/item?id=RSMUP_1994__92__59_0> © Rendiconti del Seminario Matematico della Università di Padova, 1994, tous droits réservés. L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l’ac- cord avec les conditions générales d’utilisation (http://www.numdam.org/legal. php). Toute utilisation commerciale ou impression systématique est consti- tutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Absolute Irreducibility for Finitary Linear Groups. FELIX LEINEN (*) Let V be a vector space over the field K. We denote by FGL(V) the group of all finitary Linear transformations of V, i.e., the group of all K-isomorphisms g of V satisfying Subgroups of FGL(V) are said to be finitary linear. During the last few years, these groups have been an area of intense and fruitful research, investigated by V. V. Belyaev, J. I. Hall, U. Meierfrankenfeld, R. E. Phillips, 0. Puglisi and B. A. F. Wehrfritz. Our aim here is it to carry over the machinery of absolute irreducibility from linear groups to finitary linear groups. For every field extension L/K, there is a natural action of the gen- eral linear group GL(V) on the L-space which embeds GL(V) into GL(VL ). A subgroup G of GL(V) is said to be absolutely ir- reducible if, for every field extension L/K, the vector space VL is an ir- reducible LG-module. We will extend [2, Theorem 1.19] literally to the following result about finitary linear groups. THEOREM. Let V be a vector space ov

There are no comments yet on this publication. Be the first to share your thoughts.

Statistics

Seen <100 times
0 Comments

More articles like this

Nilpotence in finitary skew linear groups

on Journal of Pure and Applied Al... Jan 01, 1992

On Nonmodular Periodic Finitary Linear Groups

on Journal of Algebra Jan 01, 2000
More articles like this..