Sylown.

/ˈsiːlɒf/

Etymology: < the name of P. L. Sylow (1832–1918), Norwegian mathematician.

Mathematics.

Used attributively and in the possessive to designate concepts in group theory propounded by Sylow ( Math. Annalen (1872) V. 584).

a. Sylow's theorem n. (see quots. 1897, 1975).

ΘΚΠ

the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem > relating to prime numbers

Fermat's theorem1811

Sylow's theorem1893

1893 Proc. London Math. Soc. 25 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.

1897 W. Burnside Theory Groups of Finite Order vi. 91 We shall divide the proof of Sylow's theorem into two parts. First we show that, if p^a is the highest power of a prime p which divides the order of a group, the group must have a sub-group of order p^a; and secondly that the sub-groups of order p^a form a single conjugate set and that their number is congruent to unity, mod. p.

1975 I. 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.

b. Sylow subgroup n. (also Sylow p-subgroup) a subgroup whose order is the largest power of the prime p which divides the order of the 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

1905 Messenger Math. XXXV. 48 A group..all of whose Sylow subgroups are cyclical.

1976 Nature 20 May p. vii (advt.) The classification of nonsoluble groups with abelian sylow 2-subgroups.

This entry has not yet been fully updated (first published 1986; most recently modified version published online September 2018).

单词	sylow
释义	Sylown. /ˈsiːlɒf/ Etymology: < the name of P. L. Sylow (1832–1918), Norwegian mathematician. Mathematics. Used attributively and in the possessive to designate concepts in group theory propounded by Sylow ( Math. Annalen (1872) V. 584). a. Sylow's theorem n. (see quots. 1897, 1975). ΘΚΠ the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem > relating to prime numbers Fermat's theorem1811 Sylow's theorem1893 1893 Proc. London Math. Soc. 25 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. 1897 W. Burnside Theory Groups of Finite Order vi. 91 We shall divide the proof of Sylow's theorem into two parts. First we show that, if p^a is the highest power of a prime p which divides the order of a group, the group must have a sub-group of order p^a; and secondly that the sub-groups of order p^a form a single conjugate set and that their number is congruent to unity, mod. p. 1975 I. 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. b. Sylow subgroup n. (also Sylow p-subgroup) a subgroup whose order is the largest power of the prime p which divides the order of the 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 1905 Messenger Math. XXXV. 48 A group..all of whose Sylow subgroups are cyclical. 1976 Nature 20 May p. vii (advt.) The classification of nonsoluble groups with abelian sylow 2-subgroups. This entry has not yet been fully updated (first published 1986; most recently modified version published online September 2018). < n.1893
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