“Coset”的概念、定义、习题解题方法及翻译-数学辞典

单词

Coset

释义

Coset

Consider a countable Subgroup with Elements and an element not in , then

(1)

(2)

for

, 2, ... are left and right cosets of the Subgroup

with respect to

. The coset of aSubgroup has the same number of Elements as the Subgroup. The Order of any Subgroup is a divisor of the Order of the Group. The originalGroup can be represented by

(3)

For a not necessarily Finite Group with a Subgroup of , define an Equivalence Relation if for some in . Then the Equivalence Classes are the left (orright, depending on convention) cosets of in , namely the sets

(4)

where

is an element of

See also Equivalence Class, Group, Subgroup

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