Question

here is the question

Answer 1

Hum...

Answer 2

Wheres the question?

Answer 3

like tf

Answer 4

XD

Answer 5

@everyone please help

Answer 6

@perl

Answer 7

i might need an abstract algebra book

Answer 8

we know that
$$ \Large \log x + \log y = \log ( x * y )$$

Answer 9

A function \( \bf f: G \to H \) from a group G to a group H is a homomorphism (or a group map) if \( \bf f(ab) = f(a)f(b)\) for all \( \bf a, b \in G \).

Answer 10

actually the only way to make this work would be to define g(x) = e^x , thats why im confused

Answer 11

exp(x + y) = exp(x) * exp(y)

Answer 12

exp(x) means \( \bf e^x \)

Answer 13

@perl

Answer 14

@perl please number 2,6,8

Answer 15

@perl

Answer 16

@perl

Answer 17

@perl

Answer 18

i dont understand how these questions are entered

Answer 19

you have the file

Answer 20

you want the kernel of e^x ?

Answer 21

yes

Answer 22

is it 0 or 1 or e

Answer 23

The kernel of a group homomorphism is the set of all elements of which are mapped to the identity element of

Answer 24

so what is the element then?

Answer 25

kernel is {0}

Answer 26

because e^0 = 1

Answer 27

what about number 5

Answer 28

i guess A

Answer 29

and al so , A bijective homomorphism is called
endomorphism
Exomorphism
Isomorphism
Automorphism

Answer 30

is it D

Answer 31

for five, did you test the possibiloities

Answer 32

let g(a) = 2a
now test
g(a+b) = g(a)g(b)

Answer 33

waw, i really wish you are my real teacher

Answer 34

thanks.

Answer 35

$$
\Large g: \mathbb{(Z,+) \to (2\mathbb{Z, +})
\\g(x) = 2x
\\
\\ \therefore \
\\
g(a+b) = 2(a+b)
\\g(a)g(b) = 2a + 2b

}

$$

Answer 36

you have to think about operations abstractly

Answer 37

thank you so much @perl .. you are a genius lol