Irreducible representations of locally polycyclic groups over an absolute field
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Abstract
Irreducible representations of locally almost polycyclic groups over an absoltue field are studied. Necessary and sufficient conditions for a solvable, locally polycyclic group of finite special rank to have a faithful irreducible representation over an absolute field are obtained.
Keywords
Irreducible Representation Special Rank Polycyclic Group Absolute Field Faithful Irreducible Representation
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Literature cited
- 1.D. I. Zaitsev, “Products of Abelian groups,” Algebra Logika,19, No. 2, 150–172 (1980).Google Scholar
- 2.J. E. Roseblade, “Group rings of polycyclic groups,” J. Pure Appl. Algebra,3, No. 3, 307–328 (1973).Google Scholar
- 3.B. A. F. Wehrfritz, “Groups whose irreducible representations have finite degree,” Math. Proc. Cambridge Phil. Soc.,5, No. 3, 411–422 (1981).Google Scholar
- 4.V. D. Mazurov, Yu. I. Merzlyakov, and V. A. Churkin (eds.), Kourovka Notebook [in Russian], 9th edition, Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk (1984).Google Scholar
- 5.A. V. Tushev, “On irreducible representations of locally polycyclic groups of finite rank,” in: International Conference on Algebra in Memory of A. I. Mal'tsev, Abstracts of Reports on Group Theory, Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk (1989), p. 125.Google Scholar
- 6.J. E. Roseblade, “Application of the Artin-Rees lemma to group rings,” Symp. Math.,17 (1976), pp. 471–478.Google Scholar
- 7.N. Bourbaki, Commutative Algebra [Russian translation], Nauka, Moscow (1971).Google Scholar
- 8.V. S. Charin, “On groups of automorphisms of nilpotent groups,” Ukr. Mat. Zh.,8, No. 3, 295–304 (1954).Google Scholar
- 9.J. S. Wilson, “Some properties of groups inherited by normal subgroups of finite index,” Math. Z.,144, No. 1, 19–21 (1970).Google Scholar
- 10.L. Fuchs, Infinite Abelian Groups, Vol. 2, Academic Press, New York (1973).Google Scholar
- 11.S. Lang, Algebra, Addison-Wesley, Reading, Massachusetts (1965).Google Scholar
- 12.N. Bourbaki, Modules, Rings, and Forms [Russian translation], Nauka, Moscow (1966).Google Scholar
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© Plenum Publishing Corporation 1991