Isomorphism

Isomorphism Quiz

Spec 1.5 · Edexcel A-Level Further Maths: Quiz

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  1. 1. Groups GG and HH are isomorphic. GG has exactly 3 elements of order 2. How many elements of order 2 does HH have?

    • A. 11
    • B. 22
    • C. 44
    • D. 33

  2. 2. Which is NOT a valid reason for two groups to be non-isomorphic?

    • A. One is abelian and the other is not
    • B. They use different symbols for the operation
    • C. One is cyclic and the other is not
    • D. They have different numbers of elements

  3. 3. An isomorphism φ:Z6→H\varphi:Z_6\to H has φ(1)=g\varphi(1)=g. What is φ(3)\varphi(3)?

    • A. g3g^3
    • B. 3g3g
    • C. g+3g+3
    • D. ee

  4. 4. Which group of order 4 is isomorphic to Z4Z_4?

    • A. {1,3,5,7}\{1,3,5,7\} under multiplication mod 8
    • B. {1,i,−1,−i}\{1,i,-1,-i\} under multiplication
    • C. {0,1,2,3}\{0,1,2,3\} under multiplication mod 4
    • D. {1,−1}×{1,−1}\{1,-1\}\times\{1,-1\}

  5. 5. An isomorphism φ:G→H\varphi:G\to H is defined with φ(g)=h\varphi(g)=h. What is the order of gg if hh has order 5?

    • A. 55
    • B. 11
    • C. It cannot be determined
    • D. 1010

Quiz