Group theory trouble

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  1. turnand's Avatar
    1 04-06-2012  14:57
    • Respected Member
    • Location: Solihull
    • Posts: 176
    Group theory trouble
    Hi, can anyone help prove this equality in group theory:

    |AB|=(|A||B|)/(|A N B|)

    Where the N denotes intersection

    Cannot assume A or B are finite
  2. nuodai's Avatar
    2 04-06-2012  15:26
    • PS Helper
    • TSR Legend
    Re: Group theory trouble
    I take it A and B are subgroups of a larger group G, say?

    If so, your best bet is actually to show that \dfrac{\left| A \right|}{\left| A \cap B \right|} = \dfrac{\left| AB \right|}{\left| B \right|}, which you can do by constructing a bijection between cosets of A \cap B in A, and cosets of B in AB.
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