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Group and subgroup example

  1. Jan 30, 2012 #1
    In an example it says that, if [itex] |G| = 15 [/itex] and [itex] G [/itex] has subgroups [itex] A,B [/itex] of [itex] G [/itex] with [itex] |A| = 5 [/itex] and [itex] |B| = 3 [/itex], then [itex] A \cap B [/itex] must equal [itex] \{e_G\} [/itex] and the smallest subgroup of [itex] G [/itex] containing both [itex] A [/itex] and [itex] B [/itex] is [itex] G [/itex] itself. Could anyone explain why? Thanks!
     
  2. jcsd
  3. Jan 30, 2012 #2

    morphism

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    Hint: Lagrange
     
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