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For #1, let be normal subgroups of orders respectively. Using the identity and the fact that we find that is a subgroup of order . Let then with this means . Therefore this group is cyclic of order .
Note, has ten elements but it is not cyclic.
For #2, let be a group of prime order. Let so that . Argue that using Lagrange's theorem.
please help me with second question last part....
Originally Posted by szpengchao please help me with second question last part.... The general result says that the subgroups of (the cyclic subgroup of order ) are precisely where is a positive divisor of . And furthermore, is a subgroup of if and only if .
For example, the complete list of subgroups of are given below.
what is the triangle in question 1, N_1 , N_2, triangle H
is that : belongs to?
Originally Posted by szpengchao what is the triangle in question 1, N_1 , N_2, triangle H
is that : belongs to? It means normal subgroup.
what does [k]_n means?
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