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Homework Help: Group question

  1. Jan 15, 2012 #1
    So I have this group G. Then I make set [itex]\overline{G}[/itex] with a new operation <[itex]\overline{G}[/itex],*> a*b=ba. Show [itex]\overline{G}[/itex] is a group,

    So showing associativity is easy. But I am unsure how to show the identities and the inverse.

    I want to same the identity is 1 but since we don't have any numbers I have a feeling that could be wrong and for the inverse just a^(-1). How do you know what is going to be what if you don't have a specific structure like the reals or the integers to work with?

    Just curious if [itex]\overline{G}[/itex][itex]\subseteq[/itex] G then would [itex]\overline{G}[/itex] retain G identity?
  2. jcsd
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