One generalization of
Fitting's theorem

B. Petrenko

Fitting's theorem (in one of its group-theorethic versions) is generalized on modules with finite composition series over the ring $DG$, where $D$ is a Dedekind domain and $G$ is an $\operatorname{XC} $-hypercentral group for some formation of finite groups $\operatorname{X}$.

1. . C.W. Curtis, I. Reiner Representation theory of finite groups and associative algebras, John Wiley ,addr New-York–1962

2. K. Doerk, H. Hawkes Finite soluble groups, Walter de Gruyter,addr Berlin–1992

3. Z.Y. Duan Extension of abelian-by-hyper-(cyclic or finite) groups// Commun. Algebra V.20–1992 N.8 p.2305–2321

4. B. Hartley, M.J. Tomkinson Splitting over nilpotent and hypercentral groups// Math. Proc. Cambridge Phil. Soc. V.78–1975 p.215–226

5. M.I. Kargapolov, Yu.I. Merzlyakov The fundamentals of the theory of groups, Springer,addr New York–1979

6. L.A. Kurdachenko, B.V. Petrenko, I.Ya. Subbotin On generalizations of some theorems of D.I. Zaitsev// Preprint 02/95, National University Los Angeles, USA

7. D.I. Zaitsev Splitting extensions of abelian groupsThe structure of groups and the properties of their subgroups, AN USSR Inst. Mat.,addr Kiev–1986 p.22–31 Russian

	One generalization of Fitting's theorem
Author	B. Petrenko Dnipropetrovsk University
Abstract	Fitting's theorem (in one of its group-theorethic versions) is generalized on modules with finite composition series over the ring $DG$, where $D$ is a Dedekind domain and $G$ is an $\operatorname{XC} $-hypercentral group for some formation of finite groups $\operatorname{X}$.
Keywords	Fitting theorem, modules with finite composition series, Dedekind domain, hypercentral group
DOI	doi:10.30970/ms.8.1.21-26
Reference	1. . C.W. Curtis, I. Reiner Representation theory of finite groups and associative algebras, John Wiley ,addr New-York–1962 2. K. Doerk, H. Hawkes Finite soluble groups, Walter de Gruyter,addr Berlin–1992 3. Z.Y. Duan Extension of abelian-by-hyper-(cyclic or finite) groups// Commun. Algebra V.20–1992 N.8 p.2305–2321 4. B. Hartley, M.J. Tomkinson Splitting over nilpotent and hypercentral groups// Math. Proc. Cambridge Phil. Soc. V.78–1975 p.215–226 5. M.I. Kargapolov, Yu.I. Merzlyakov The fundamentals of the theory of groups, Springer,addr New York–1979 6. L.A. Kurdachenko, B.V. Petrenko, I.Ya. Subbotin On generalizations of some theorems of D.I. Zaitsev// Preprint 02/95, National University Los Angeles, USA 7. D.I. Zaitsev Splitting extensions of abelian groupsThe structure of groups and the properties of their subgroups, AN USSR Inst. Mat.,addr Kiev–1986 p.22–31 Russian
Pages	21-26
Volume	8
Issue	1
Year	1997
Journal	Matematychni Studii
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One generalization of Fitting's theorem