Recent content by vedicguru

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    Proving G is Cyclic if No Subgroups Other than G and {e} Exist

    ohh yeah I am sorry about that...I was in hurry or something to write it down! but yeah I believe everything else is fine and I would not forget to mention that <a> is not equal to {e}..it is G! Thanks!
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    Proving G is Cyclic if No Subgroups Other than G and {e} Exist

    oh yeah sure! I meant how would say, after constructing it! I forgot it is equal to {e} it is equal to G...this is what I get! We could say that, let a E G - {e} then we construct <a> = a, a^2, a^3... a^n=1 <- cyclic subgroup generated by element a. Since <a> is subgroup, it must coincide with G...
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    Proving G is Cyclic if No Subgroups Other than G and {e} Exist

    how do I construct <a> ??
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    Proving G is Cyclic if No Subgroups Other than G and {e} Exist

    Homework Statement Prove that if a group G has no subgroup other than G and {e}, then G is cyclic... Homework Equations The Attempt at a Solution we could say that, let a E G - {e} then we construct <a>...