certificate
(1)
p
b)
p
c
=
a
p
(b)
p
c)
A, b and c belong to z2.
Prove the existence of unit element 3
It is proved that A has an inverse a- 1, which makes A
p
a- 1
=
a- 1
p
a
=
Unit element, (where a- 1 refers to the inverse of a, written as-1 power of a) If z and operation p satisfy the above three conditions, then z and operation p can form a group. The proof is as follows: 1.
For any A, B and C belong to Z, there are: (A
p
b)
p
c=(a+b-2)
p
c=(a+b-2)+c-2=a+(b+c-2)-2=a
p
(b+c-2)=a
p
(b)
p
c)2
It is easy to know that there are two belonging to Z, so for any A belonging to Z, there are two.
p
a
=
2+a-2
=
alcoholic anonymous
p
2
=
a+2-2
=
A has the unit element 2, so it is 2.
p
a
=
a
p
2
=
a3
It is easy to know that a has an inverse 4-A, which makes: a.
p
(4-a)
=(4-a)
p
a
=
2z and operation p satisfy the above three conditions, so z and operation p can form a group.