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Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 2, Pages 438–443 (Mi smj1187)  
This article is cited in 6 scientific papers (total in 6 papers)

On some elementary properties of soluble groups of derived length 2

N. S. Romanovskiia, E. I. Timoshenkob

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University of Architecture and Civil Engineering
Full-text PDF (187 kB) Citations (6)
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Abstract: Conditions are found for a soluble group of derived length 2 with few relations to be universally equivalent to a free soluble group of derived length 2. The Fitting radical of a soluble group of derived length 2 with few relations coincides with the derived subgroup. Also, if an $n$-generator soluble group is elementarily equivalent to a free soluble group of rank $m$ and derived length $k$ then for $k=2$ or $k>2$ and $n=m$ the groups are isomorphic.
Keywords: group, soluble, derived subgroup, elementary theory.
Received: 16.12.2002
English version:
Siberian Mathematical Journal, 2003, Volume 44, Issue 2, Pages 350–354
DOI: https://doi.org/10.1023/A:1022949224145
Bibliographic databases:
UDC: 512.5
Language: Russian
Citation: N. S. Romanovskii, E. I. Timoshenko, “On some elementary properties of soluble groups of derived length 2”, Sibirsk. Mat. Zh., 44:2 (2003), 438–443; Siberian Math. J., 44:2 (2003), 350–354
Citation in format AMSBIB
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\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 2
\pages 350--354
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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