How many subgroups does Z20 have? List a generator for each ofthese subgroups. Suppose that G = <a> and |a| = 20. How manysubgroups does G have? List a generator for each of these subgroups.

Q: Which of the following are subgroups of the group Z×11: {1,3,4,5,9}, {1,3,5,7,8}, {1,8},  {1,10},…

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Q: Find a subgroup of S4 which contains six elements. How many subgroups of order six are there in S4?

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Q: If a is a group element of infinite order, what is a generator of the subgroup &lt;am&gt;…

A: The objective of the question is to find the generator of the subgroup &lt;a^m&gt; &lt;a^n&gt; where…

Q: ow many subgroups of order 3 does D3 have? Write a number of subgroups only.

A: D3={1 , r , r2 , f , rf , r2f }  Or=3 Of=2    rmf=frn-m   n=3 , 0≤m≤3 O(rif)=2   0≤i≤2 3-order…

Q: Show that the elements of S9 which send the numbers 2, 5, 7 among themselves form a subgroup of S9.…

A: 1. **Closure**: If any two permutations send 2, 5, and 7 among themselves, their composition must…

Q: 3. How many cyclic subgroups does S3 have?

A: The objective is to find the number of cyclic subgroups of S3. Subgroups of S3 are, H1=IH2=I, 1…

Q: find the number of elements in the indicated cyclic group. the cyclic subgroup of Z30 generated by…

A: To find the number of elements in the cyclic subgroup  generated by 25, you need to determine all…