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Solvable groups of finite non-Abelian rank

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Abstract

The concept of the non-Abelian rank of a group is introduced. Solvable groups of finite non-Abelian rank are studied and it is proved that their (special) rank is finite.

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Literature cited

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    A. I. Mal'tsev, “On groups of finite rank,” Mat. Sb.,22, No. 2, 351–352 (1948).

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    O. Yu. Dashkova, “Groups of finite non-Abelian rank,” in: Materials of the 24th All-Union Scientific Student Conference: Mathematics, Novosibirsk University, Novosibirsk (1986), pp. 14–17.

  3. 3.

    O. Yu. Dashkova, “On groups of finite non-Abelian rank,” in: 19th All-Union Algebra Conference: Abstracts of Reports, Part 2, Institute of Applied Problems of Mechanics and Mathematics, Academy of Sciences of the UkrSSR, Lvov (1987), pp. 81–82.

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    B. Huppert, Endliche Gruppen I, Springer, Berlin (1967).

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    P. Hall, “On the finiteness of certain solvable groups,” in: Solvable and Simple Infinite Groups [Russian translation], Mir, Moscow (1981), pp. 171–206.

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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 159–164, February, 1990.

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Dashkova, O.Y. Solvable groups of finite non-Abelian rank. Ukr Math J 42, 140–144 (1990). https://doi.org/10.1007/BF01071005

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Keywords

  • Solvable Group