| 中文摘要 |
Kokata親屬制的連婚圈由四條父系線或母系線所構成。各線間舉行隔二世代的雙方交表婚，因而產生 I, f2m, fm2, fmf, m, m2, f, f2, fm, fmfm, mf, f2m2 等分節。以分節為元的集合具有m3 = f3 = （fm2）2 = I的群論關係。十二個分節中有四個自反元 I,f2m, fm2, fmf 及四組正反對（f, f2）, （m, m2）, （fm, fmfm）, （mf, f2m2）. f-循環子群（I, f, f2）的右分解得代表四條母系線的陪集,m-循環子群（I, m, m2）的左分解得代表四條父系線的陪集。單位元以外的三個共軛類代表三個不同的世代。正規子群由屬於自我世代的四個自反元所構成與Klein的四元群同構。交換子群、共軛子群均與正規子群相等。因子群由以正規子群為模數而得的三個陪集為元，各陪集由不同世代分節的集合而成。 |
| 英文摘要 |
From Elkin's diagram we deduce that the Kokata tribe practices bilateral cross-cousin marriage in a connubium of four hordes with three segments in each one and that the defining relations for the corresponding group of twelve elements may be given by m3 = f3= (fm2)2 = I. There are four self-inverse elements I, f2m, fm2, fmf and four inverge pairs (f, f2), (m, m2) (fm, fmfm), (mf，f2m2). The right-cosets of the cyclic subgroup (I, f, f2) are the four matrilines and the left-cosets of (I, m, m2) are the four patrilines. The three conjugate classes represent the three generations. The four self-inverse elements (i. e. ego's generation) form a normal subgroup (the commutator subgroup) which isomorphic to the Klein four-group, i. e. to the Kariera system. The corresponding factor group consists of the three generations. |
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