Abstract Algebra Answers

there exists a field with 99 element .true or fasle prove

show that x2+x+4 is irreducible over Z11.

How 2×2 matrix with components A B C D . Transform under So (2)

Q. What is sub-ring? Write its two example.

Which of the following are binary operations. Justify your answer.
i) The operation · defined on Q by a·b = a(b− 1).
ii) The operation · defined on [0,π] by x·y = cosxy.
Also, for those operations which are binary operations, check whether they are
associative and commutative.

If
B=ab
such that a, b are integers , then B is a set of _____numbers

Q. Prove that two conjugate sub-groups have same order.

Q. What is difference b/w homomorphism and homeomorphism?

Q. (i) what is P-group?
(ii) Define order of P-group.

Q.Prove that two conjugate groups have same order.