MCQs of Algebraic Structures (Discrete Mathematics - 3140708)

Showing 41 to 50 out of 65 Questions

41.

For

G = (ℤ_{6}, +_{6})

, how many generators of the cyclic group G?

42.

How many subgroups of the symmetric group

(S_{3}, \circ)

43.

How many subgroups of the group

G = (ℤ_{12}, +_{12}) ?

44.

How many subgroups of the group

G = (ℤ_{30}, +_{30}) ?

45.

Let

G = ({ℤ_{10}}^{*}, \times_{10})

then o(G) is _____.

46.

Let

G = ({ℤ_{7}}^{*}, \times_{7})

be a group then the inverse of the elements 2, 3 and 6 are _____.

47.

Let

G = ({ℤ_{7}}^{*}, \times_{7})

be a group then the order of the sub group of G generated by 2 is _____.

48.

Which of the following is incorrect?

(a)	Let (H, ) be a subgroup of (G, ) then for $a \in G$ , aH={a*h/ $h \in H$ } is called left coset of H in G.
(b)	No left or right coset can be empty.
(c)	A and B both
(d)	none

49.

Let (H, *) be a subgroup of (G, *) then which of the following is incorrect?

(a)	Ha and aH both are subsets of G for $a \in G$ .
(b)	$a \in H iff aH = H .$
(c)	If G is non Abelian then every subgroup of G is non Abelian.
(d)	none

50.

A subgroup H of a group G is said to be normal subgroup of G if

\forall a \in G & \forall h \in H such that

_____.

Showing 41 to 50 out of 65 Questions