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let us assume G is not cyclic. Let a be an element of G of maximal order. Since G is not cyclic we have <a>≠G. Let b be an element in G, but not in the cyclic subgroup generated by a.

O(a) = m and O(b) = n where O() refers tothe orders. . then how can we use this to construct a subgroup of G isomorphic to Zp×Zp?

Help will be appreciated. Thank you

O(a) = m and O(b) = n where O() refers tothe orders. . then how can we use this to construct a subgroup of G isomorphic to Zp×Zp?

Help will be appreciated. Thank you