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### MTH633 - Group Theory MCQs

MTH633 Midterm Solved MCQsMTH633 Midterm MCQs Info
Post TitleMTH633 Midterm MCQs
Book CodeMTH633
DegreeBSIT/BSCS/Other
UniversityVirtual Univerity of Pakistan
MTH633 MidtermMTH633 Midterm Solved MCQs
Mid/FinalMTH633 Midterm MCQs
Also, ReadMTH633 Quiz 1 Solved MCQs

## MTH633 Midterm Solved MCQs

Let  H be a subgroup of G and a in G f (H = aHa)-1 then.  (MTH633)

aH=H

aH=Ha

aH=G

Ha=H

If G is a finite group and H is a subgroup of G then [H] divides [G].  (MTH633)

Inversion theorem

Lagrange theorem

Sylow theorem

Cayley theorem

Let : G-H be a homomorphism then (a-1) = (a)-1 for a E G.  (MTH633)

True

False

Suppose H and K are finite subgroups of finite group G such that K<H<G and (G,H) and (H,K) is finite [G,K] is equal to.  (MTH633)

(H:K)(G:H)

(G:K)x(H:K)

(G:H)(H:K)

(G:H)(H:K)

The group O is a copy of the group H2 if the function f : G-H is ………….(MTH633)

Homomorphic

Onto

Isomorphic

Objective

Which statement is true?  (MTH633)

If G is a finite group and H is a subgroup of G then [G] divides [H]

If G is a finite group and H is a subgroup of G then [H] divides [G]

If G is a finite group and H is a subgroup of G then [G] divides [H]

If G is a finite group and H is a subgroup of G then [H] multiples [G]

Let H be a subgroup of G and a,b in o. If a belongs to bH then.  (MTH633)

$(\rm[aH = bH])$

$(\rm[bH = H])$

$(\rm[H=aH])\[(RM[a])^[-1])$

$(\rm[aH = H])$

If G is a finite group and H is a subgroup of G then [H] divides [G].  (MTH633)

Inversion theorem

Lagrange theorem

Sylow theorem

Cayley theorem

The group O is a copy of the group H2 if the function f : G-H is ………….(MTH633)

Homomorphic

Onto

Isomorphic

Bijective

Let :G - H be an isomorphism then if AG is abelian then H is not abelian.  (MTH633)

True

False

Let G be a group then a bijective homomorphism group is.  (MTH633)

Injective group

Automorphic group

Bijective group

Isomorphic group

If G is finite then indices of H in G are finite and (G,H) is equal to.  (MTH633)

[G]x[G]

[H]\[G]

[G]x[H]

[G]/[H]

Let                        SE

SE

Z2

Be a symmetric group on n elements let function f form to be homomorphism then f is 0 if it is - permutation 2f is 1 if it is - permutation.  (MTH633)

Even, even

Let H be a subgroup of G and a,b,in G. if a belongs to H then.  (MTH633)

Ha = H

bH = Hb

aH = H

bH = H

Let G be a group then a bijective homomorphism group is.  (MTH633)

Bijective group

Isomorphic group

Injective group

Automorphic group

The converse of Lagrange's theorem holds for abelian groups.  (MTH633)

True

False

Which statement is true?  (MTH633)

If G is a finite group and H is a subgroup of G then [G] divides [H]

If G is a finite group and H is a subgroup of G then [H] divides [G]

If G is a finite group and H is a subgroup of G then [G] divides [H]

If G is a finite group and H is a subgroup of G then [H] multiples [G]