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A graphic construction of the collection formula for certain types of groups

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Abstract

Procedures for calculating P. Hall's famous collection formula for metabelian and two types of transmetabelian groups are described. Complicated combinatorial calculations are based on graphs corresponding to basic monomials. In conclusion programs written in PASCAL are given.

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References

  1. M. Hall, The Theory of Groups, MacMillan, New York (1959).

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  2. A. I. Skopin, “Realization of computer calculations in transmetabelian groups,” Vestnik Leningrad. Univ. Ser. 1, No. 1, 20–23 (1988).

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  3. A. I. Skopin, “On the collection formula,” Zap. Nauchn. Sem. Leningrad. Otd. Mat. Inst. Steklov. (LOMI),74, 59–63 (1974).

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  4. N. N. Lyashenko and A. I. Skopin, “Finding graphically on a computer P. Hall's collection formula for certain 2-generated groups,” XIX All-Union Algebraic Conference, Theses and Reports [in Russian], Part 1, L'vov (1987), p. 168.

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Authors
  1. A. I. Skopin
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 191, pp. 140–151, 1991.

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Skopin, A.I. A graphic construction of the collection formula for certain types of groups. J Math Sci 63, 693–699 (1993). https://doi.org/10.1007/BF01097984

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  • DOI: https://doi.org/10.1007/BF01097984

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