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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
Also, ReadMTH104 Quiz 1 Solved


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)

Add, even 

Even, even 

Even, add 

Add, add


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]



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MTH633 Midterm MCQs

MTH633 Midterm MCQs


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