| 单词 | factor group |
| 释义 | > as lemmasfactor group factor group n. [after German †Factorgruppe (O. Hölder 1889, in Mathematische Annalen 34 28; now Faktorgruppe)] Mathematics a group G/N, the elements of which are the cosets in a given group G of a normal subgroup N of G; also called quotient group. ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > in abstract algebra > groups syntheme1844 group1854 substitution group1861 quaternion group1881 subgroup1881 Abelian group1892 permutation group1893 quotient group1893 factor group1895 order1897 symmetric group1897 point group1903 Sylow subgroup1905 module1927 Lie group1939 symmetry group1956 Weyl group1961 stabilizer1965 1895 Bull. Amer. Math. Soc. 1 234 The proof, as given by Hölder, that the factor-groups are constant for all the series of composition of a group, easily follows by induction. 1965 E. M. Patterson & D. E. Rutherford Elem. Abstr. Algebra ii. 49 If G is a finite group of order m and H is a normal subgroup of order n, then..the factor group G/H is a finite group of order m/n. 2008 M. S. Dresselhaus et al. Group Theory i. 11 The order of the factor group is the index of the self-conjugate subgroup. < as lemmas |
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