Let H be a subgroup of a group G and a,b∈G. Then a∈bH if and only if 1) ba−1∈H 2) ba∈H 3) b−1a∈H 4) None of these

Given: H be a subgroup of a group G. i.e. H⊆G. and a,b∈G If a∈bH (1) b∈bH ⇒b1∈bH(∴a∈G⇒a1∈G) (2) Now from eq-n (1) and (2) a∈bH and b1∈bH then b1a∈b1(bH) b1a∈(b1b)H b1a∈H

Expert Answer to "Let H be a subgroup of a group..."

College
Algebra
Abstract algebra

Siena Duran

Answered question

2022-02-12

Let H be a subgroup of a group G and

a, b \in G

. Then

a \in b H

if and only if
1)

b a - 1 \in H

b a \in H

b - 1 a \in H

4) None of these

Answer & Explanation

Johnathan Carpenter

Beginner2022-02-13Added 12 answers

Given:
H be a subgroup of a group G.
i.e.

H \subseteq G

.
and

a, b \in G

a \in b H

(1)

b \in b H

\Rightarrow b^{1} \in b H (∴ a \in G \Rightarrow a^{1} \in G)

(2)
Now from eq-n (1) and (2)

a \in b H and b^{1} \in b H

then

b^{1} a \in b^{1} (b H)

b^{1} a \in (b^{1} b) H

b^{1} a \in H

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Abstract algebra

How to find out the mirror image of a point?
Generators of a free group
If G is a free group generated by n elements, is it possible to find an isomorphism of G with a free group generated by n-1 (or any fewer number) of elements?
How many 3/4 Are in 1
Convert 10 meters to feet. Round your answer to the nearest tenth
6. Reduce the following matrix to reduced row echelon form:
$C equals open parentheses table row 1 cell negative 1 end cell cell 1 half end cell cell 1 half end cell row 0 1 cell 1 half end cell cell negative 1 half end cell row 0 0 1 0 row 0 0 0 0 end table close parentheses$
Let v be a vector over a field F with zero vector 0 and let s,T be a substance of V .then which of the following statements are false
Describe Aut(Zp), the automorphism group of the cyclic group Zp where p is prime. In particular find the order of this group. (Hint: A generator must map to another generator)

Didn't find what you were looking for?