- set of G into disjoint, equal-size
subsets called cosets.
There are left
cosets and
right cosets.
Cosets (both left and right) have the same
number of elements...
- If K = {1}, then H \ G / K = H \ G. A
double coset HxK is a
union of
right cosets of H and left
cosets of K; specifically, HxK=⋃k∈KHxk=∐Hxk∈H∖HxKHxk...
- In mathematics,
coset enumeration is the
problem of
counting the
cosets of a
subgroup H of a
group G
given in
terms of a presentation. As a by-product...
-
subgroup H in a
group G is the
number of left
cosets of H in G, or equivalently, the
number of
right cosets of H in G. The
index is
denoted | G : H | {\displaystyle...
- In
coding theory, a
coset leader is a word of
minimum weight in any
particular coset - that is, a word with the
lowest amount of non-zero entries. Sometimes...
- left
coset of H
decomposes into [ H : K ] {\displaystyle [H:K]} left
cosets of K.
Since G
decomposes into [ G : H ] {\displaystyle [G:H]} left
cosets of...
-
normal subgroup.
Every subgroup of
index 2 is normal: the left
cosets, and also the
right cosets, are
simply the
subgroup and its complement. More generally...
- {\displaystyle N} . Due to the
normality of N {\displaystyle N} , the left
cosets and
right cosets of N {\displaystyle N} in G {\displaystyle G} are the same, and...
-
correspond to the left
cosets G/Ho, and the
marked point o
corresponds to the
coset of the identity. Conversely,
given a
coset space G/H, it is a homogeneous...
-
apply to the
right cosets of H {\displaystyle H} . The left
cosets of H {\displaystyle H} may or may not be the same as its
right cosets. If they are (that...
