Abstract
An algebraic representation of operations of genetic recombinations is illustrated. It is shown that the recombinations between chromosomes in the two-strand model can be represented by groups, in the sense of the theory of groups. Recombinations between chromosomes with inversions and a translocation are considered as well as cases without them. It is found that the groups derived from such cases are Abelianp-groups (p=2) and that the types of the Abelian groups for the various pairs of chromosomes are different from each other.
Differences among those recombination groups are illustrated by showing the sets of generators of the various groups, which generate the corresponding recombination groups by multiplication.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Bailey, N. T. J. 1961.Introduction to The Mathematical Theory Linkage. Oxford: The Clarendon Press.
Coxeter, H. S. M. and W. O. J. Moser. 1957.Generators and Relations for Discrete Groups. Berlin: Springer Verlag.
Kurosh, A. G. 1955.The Theory of Groups, I. (Eng. trans.) New York: Chelsea Pub. Co.
— 1956.The Theory of Groups, II. (Eng. trans.) New York: Chelsea Pub. Co.
Zassenhaus, H. 1937.Lehrbuch der Gruppentheorie, I. Leipzig and Berlin: Verlag und Druck von. B. G. Teubner.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shikata, M. Group representation of genetic recombinations. Bulletin of Mathematical Biophysics 26, 91–100 (1964). https://doi.org/10.1007/BF02476626
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02476626