Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-18T21:16:05.305Z Has data issue: false hasContentIssue false
  • English
  • Français

The centralizer poset in groups of semilinear maps

Published online by Cambridge University Press:  26 February 2010

B. A. F. Wehrfritz
B. A. F. Wehrfritz
Affiliation:
Department of Mathematics, Queen Mary College, London E1 4NS.
Get access

Extract

Let M be a finitely generated module over the finitely generated abelian group U. Denote the group of all semilinear maps of M by SautUM, a ℤ-automorphism g of M being semilinear if there exists an automorphism γ of U, called an auxiliary automorphism of g, such that mug = mguγ for all m ∊ M and u ∊ U.

Type
Research Article
Information
Mathematika , Volume 25 , Issue 2 , December 1978 , pp. 251 - 263
Copyright
Copyright © University College London 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Lennox, J. C. and Roseblade, J. E., “Centrality in finitely generated soluble groups”, J. Algebra, 16 (1970), 399–435.CrossRefGoogle Scholar
2.Roseblade, J. E., “Prime ideals in grouprings of polycyclic groups”, Proc. London Math. Soc., (3), 36 (1978), 385–447.CrossRefGoogle Scholar
3.Wehrfritz, B. A. F.. “Remarks on centrality and cyclicity in linear groups”, J. Algebra, 18 (1971), 229–236.CrossRefGoogle Scholar
4.Wehrfritz, B. A. F.. Infinite Linear Groups (Springer, Berlin-Heidelberg-New York, 1973).CrossRefGoogle Scholar
5.Wehrfritz, B. A. F.. “Representations of holomorphs of group extensions with abelian kernels”, Math. Proc. Camb. Phil. Soc., 78 (1975), 357–368.CrossRefGoogle Scholar
6.Wehrfritz, B. A. F.. “Finitely generated groups of module automorphisms and finitely generated metabelian groups”, Symp. Math., 17 (1976), 261–275.Google Scholar
7.Wehrfritz, B. A. F.. “Automorphism groups of Noetherian modules over commutative rings”, Arch. Math. (Basel), 27 (1976), 276–281.CrossRefGoogle Scholar
8.Wehrfritz, B. A. F.. “Nilpotence in groups of semilinear maps I”, Proc. London Math. Soc., (3), 36 (1978), 448–479.CrossRefGoogle Scholar
9.Wehrfritz, B. A. F.. “Nilpotence in groups of semilinear maps II”, J. London Math. Soc., (2), 16 (1977), 449–457.CrossRefGoogle Scholar
10.Wehrfritz, B. A. F.. “Nilpotence in groups of semilinear maps III”, J. Pure App. Algebra, to appear.Google Scholar
11.Wehrfritz, B. A. F.. “On the Lie-Kolchin-Mal'cev Theorem”, J. Austral. Math. Soc., (Series A), 26 (1978), 270–276.CrossRefGoogle Scholar