- #1

- 24

- 0

Let G be any group, and let a, b ∈ G. Show that there are c, d ∈ G such that ac = b and da = b. Hint: you have to give an explicit definition for c and d in terms of a and b.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter patelnjigar
- Start date

- #1

- 24

- 0

Let G be any group, and let a, b ∈ G. Show that there are c, d ∈ G such that ac = b and da = b. Hint: you have to give an explicit definition for c and d in terms of a and b.

- #2

mathwonk

Science Advisor

Homework Helper

2020 Award

- 11,123

- 1,323

what have you tried?

- #3

- 24

- 0

Let G be any group, and let a, b ∈ G. Show that there are c, d ∈ G such that ac = b and da = b. Hint: you have to give an explicit definition for c and d in terms of a and b.

- #4

morphism

Science Advisor

Homework Helper

- 2,015

- 4

(i) if x is in G, then so is its inverse

(ii) if x,y are in G, then so is xy

- #5

- 24

- 0

GIVE a, b ∈ G

SHOW c, d ∈ G ???

ac=b da=b

ac=b ---> proof: a (a^(-1)b)=b (IS THAT RIGHT? I THINK SO AND THAT'S RIGHT)

da=b ---> proof: ???

- #6

- 24

- 0

proof: a (a^(-1)b)=b

uniqueness

if ac=ad=b

then c=d (left Cancellation)

How do I slove for da=b?? I need for that..

- #7

morphism

Science Advisor

Homework Helper

- 2,015

- 4

Same idea: let d = ba^(-1).

- #8

- 24

- 0

ac=b

a (a^(-1)b)=b, if ac=ad=b, then c=d (left cancellation).. I m sure that's right.

da=b

d=ba(a^(-1)), if ad=ac=b, then d=c (right cancellation) is that right?????

Share: