Q. Let (A7, ⊗7)=({1, 2, 3, 4, 5, 6}, ⊗7) is a group. It has two sub groups X and Y. X={1, 3, 6}, Y={2, 3, 5}. What is the order of union of subgroups?

View solution

Q. A relation (34 × 78) × 57 = 57 × (78 × 34) can have __________ property.

View solution

Q. B₁: ({0, 1, 2….(n-1)}, xₘ) where xₘ stands for “multiplication-modulo-n” and B₂: ({0, 1, 2….n}, xₙ) where xₙ stands for “multiplication-modulo-m” are the two statements. Both B₁ and B₂ are considered to be __________

View solution

Q. If group G has 65 elements and it has two subgroups namely K and L with order 14 and 30. What can be order of K intersection L?

View solution

Q. Consider the binary operations on X, a*b = a+b+4, for a, b ∈ X. It satisfies the properties of _______

View solution

Q. Let * be the binary operation on the rational number given by a*b=a+b+ab. Which of the following property does not exist for the group?

View solution

Q. Let G be a finite group with two sub groups M & N such that |M|=56 and |N|=123. Determine the value of |M⋂N|.

View solution

Q. A group G, ({0}, +) under addition operation satisfies which of the following properties?

View solution

Q. If (M, *) is a cyclic group of order 73, then number of generator of G is equal to ______

View solution

Q. The set of even natural numbers, {6, 8, 10, 12,..,} is closed under addition operation. Which of the following properties will it satisfy?

View solution

Q. In a group there must be only __________ element.

View solution

Q. _____ is the multiplicative identity of natural numbers.

View solution

Q. An identity element of a group has ______ element.

View solution

Q. __________ matrices do not have multiplicative inverses.

View solution

Q. If X is an idempotent nonsingular matrix, then X must be ___________

View solution

Q. If A, B, and C are invertible matrices, the expression (AB⁻¹)⁻¹(CA⁻¹)⁻¹C2 evaluates to ____________

View solution

Q. If the sum of elements in each row of an n×n matrix Z is zero, then the matrix is ______________

View solution

Q. ___________ are the symmetry groups used in the Standard model.

View solution

Q. A semigroup S under binary operation * that has an identity is called __________

View solution

Q. An element a in a monoid is called an idempotent if ______________

View solution