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Math Help - GROUP theory

  1. #1
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    GROUP theory

    Let Z(G) denote the center of a group G, then the order of a quotient group G/Z(G) cannot be
    a) 4
    b) 6
    c) 15
    d) 25

    please send me the answer with solution.
    bye


    Let G be a finite group and Z(G) be a normal subgroup.
    Then the quotient group Z(G) of G is ( |G| / |Z(G)| ).Here O(G) divides the O(Z(G)) .So we can take 15(factors 1,3,5,15) and 25(factors 1,5,25).SO the ans. would be (a) and ( b).
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  2. #2
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    Quote Originally Posted by cdniki View Post
    Let Z(G) denote the center of a group G, then the order of a quotient group G/Z(G) cannot be
    a) 4
    b) 6
    c) 15
    d) 25

    please send me the answer with solution.
    bye


    Let G be a finite group and Z(G) be a normal subgroup.
    Then the quotient group Z(G) of G is ( |G| / |Z(G)| ).Here O(G) divides the O(Z(G)) .So we can take 15(factors 1,3,5,15) and 25(factors 1,5,25).SO the ans. would be (a) and ( b).

    The quotient group G/Z(G) cannot be cyclic non-trivial, so the answer is...

    Tonio
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