| 释义 |
coset Math.|ˈkəʊsɛt|
Also co-set.
[f. co- 4 + set n.2]
A set composed of all the products obtained by multiplying, on the right or on the left, each element of a subgroup in turn by one particular element of the group containing the subgroup.
1910G. A. Miller in Q. Jrnl. Math. XLI. 382 If H represents any sub-group of the group G, all the operators of G may be represented..in either of the following two ways: G = H + HS2 + HS3 + {ddd} +HSγ = H + T2H + T3H + {ddd} +TγH. If for each co-set HSα (α = 2, 3, {ddd}, γ) it is possible to find some co-set TβH such that the totality of the operators HSα coincide with that of TβH, then H is an invariant sub-group of G. 1911― in Trans. Amer. Math. Soc. XII. 326 The sets HSα, SαH (α = 2, 3, {ddd}, ρ) have been called Nebengruppen or co-sets of G as regards H, the former being called the right co-sets and the latter the left co-sets. 1941Birkhoff & MacLane Survey Mod. Algebra vi. 146 We now come to a far-reaching concept of abstract group theory: the idea that any subgroup S of a group G decomposes G into cosets. 1973W. Ledermann Introd. Group Theory ii. 33 The cosets Hx and Hy are identical if and only if xy-1 {elem} H. Any two cosets are either identical or else have no element in common. 1984C. C. Sims Abstract Algebra iii. 99 Let f : G → H be a homomorphism of groups. Then the kernel N of f is a normal subgroup of G, and two elements of G are mapped to the same element of H if and only if they are in the same coset of N. |