Question

Let G be a group. Let
H is a subset of  G. Then H is a subgroup of G if the following conditions are
true
(1) e belongs to H (where e is the identity of G).
(2) if h, k belongs to H then hk belongs to H (H is closed).
(3) if h belongs to H then h inverse belongs to H.

what does it mean by h inverse???

Answer 1

if \(h\in H\) then the inverse of \(h\) is an element \(h^{-1}\) such that \(h\times h^{-1}=e\)

Answer 2

ok!!! thank you

Answer 3

some examples of common inverses

addition
a+(-a) = 0
here 0 is the identity because x+0 = x
so the additive inverse of a would be -a

multiplication
a*1/a = 1
here 1 is the identity because 1*x = x
so the multiplicative inverse of a is a/a

function composition
f(x), then f inverse is the unique function such that f(g(x)) = x and g(f(x)) = x
here f(x) = x is the identity because f(x) composed with x is just f(x)

Answer 4

that should say
"so the multiplicative inverse of a is 1/a"