Mathematics, 01.11.2019 03:31 sbhunsaker9722
Let h and k be subgroups of a group g, and let g be an element of g. the set 
is called a double coset. do the double cosets partition g?
Answers: 3
. We say that 
if, and only if, 
, or, equivalently, if 
, for some 
.
for all 
.) Note that we can write 
, where 
is the identity element, so 
and then 
. Therefore, 
.) If 
for some 
and 
. Multiplying by the inverses of h and k we get that 
and is known that 
and 
. This means that 
or, equivalently, 
, then 
.) If 
and 
such that 
and 
. Then, 
where 
and 
. Consequently, 
.
" is an equivalence over G, we use the fact that the different equivalence classes partition G. Since the equivalence classes are defined by ![[x]=\{y\in G\colon x\sim y\} =\{y\in G \colon y=hgk\ \text{for some } h\in H, k\in K \}=HxK](/tpl/images/0355/1781/f529f.png)
, then we're done.
Other questions on the subject: Mathematics
Mathematics, 21.06.2019 18:00, arianaguerin
Janie has $3. she earns $1.20 for each chore she does and can do fractions of chores. she wants to earn enough money to buy a cd for $13.50. write an inequality to determine the number of chores, c, janie could do to have enough money to buy the cd.
Answers: 1
Mathematics, 22.06.2019 07:30, PuppyLover3479
Elena's aunt bought her a $150 savings bond when she was born when elena is 20 years old the bond will have earned 105% in intrest how much will the bond be worth when elena is 20 years old
Answers: 1
You know the right answer?
Let h and k be subgroups of a group g, and let g be an element of g. the set [tex]\math hgk = \{x \i...
Questions in other subjects:
Mathematics, 20.12.2019 23:31
