| 单词 | Sylow |
| 释义 | Sylow Math.|ˈsiːlɒf|
The name of P. L. Sylow (1832–1918), Norwegian mathematician, used attrib. and in the possessive to designate concepts in group theory propounded by him (Math. Annalen (1872) V. 584), as Sylow (p-)subgroup, a subgroup whose order is the largest power of the prime p which divides the order of the group; Sylow's theorem (see quots. 1897, 1975).
1893Proc. Lond. Math. Soc. XXV. 14 It is then shown that Sylow's theorem leads to relations between the numbers of operations of different orders which it is impossible to satisfy. 1897W. Burnside Theory of Groups of Finite Order vi. 91 We shall divide the proof of Sylow's theorem into two parts. First we show that, if pa is the highest power of a prime p which divides the order of a group, the group must have a sub-group of order pa; and secondly that the sub-groups of order pa form a single conjugate set and that their number is congruent to unity, mod. p. 1905Messenger Math. XXXV. 48 A group..all of whose Sylow subgroups are cyclical. 1975I. Stewart Concepts Mod. Math. vii. 104 The best that can be said in general is Sylow's theorem; if h is a power of a prime and divides the order of a group G, then G has a subgroup of order h. 1976Nature 20 May p. vii (Advt.), The classification of nonsoluble groups with abelian sylow 2-subgroups. |
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