Abstract
Group theory and the theory of relations are used to study the kinship of certain kinds of primitive societies. It will be shown that these societies partition their members into classes that are permuted by the relations “class X has fathers (mothers) in class Y” so as to form a regular permutation group. A mathematical characterization of the conditions under which groups become relevant for the study of kinship is given and is related to the theory of structural balance. It is argued that the concept of group extension and its specialization to direct and semidirect products determine the evolutionary sequences and the coding of these kinship systems. These predictions are found to be consistent with certain observed changes, geographical distribution, and habits of usage of the kinship systems under consideration. Generalizations to aspects of behavior outside of kinship are briefly discussed.
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