Am I right in stating the following? Question: List all the subgroups of (Z 6 ,+

Question

Am I right in stating the following? Question: List all the subgroups of (Z6,+) It has only 4 subgroups. Since Z6 =( [0],[1],[2],[3],[4],[5,]) and this is an addictive group, so<[2]>={[0x2],[1x2],[2x2],[3x2]......[nx2]={[0],[2],[4]} [3x2]=[6]=[0] The subgroups are thus, <[0]>= {0} <[1]>= Z6 <[2]>={[0],[2],[4]} <[3]>={[0],[3]} <[4]>={[0],[2],[4]} <[5]>=Z6 That is 1)<[0]>= {0} 2)<[1]>=<[5]>= Z6 3)<[2]>=<[4]>={[0],[2],[4]} 4)<[3]>={[0],[3]} so there's only 4 subgroups. Am I right in stating the following? Question: List all the subgroups of (Z6,+) It has only 4 subgroups. Since Z6 =( [0],[1],[2],[3],[4],[5,]) and this is an addictive group, so<[2]>={[0x2],[1x2],[2x2],[3x2]......[nx2]={[0],[2],[4]} [3x2]=[6]=[0] The subgroups are thus, <[0]>= {0} <[1]>= Z6 <[2]>={[0],[2],[4]} <[3]>={[0],[3]} <[4]>={[0],[2],[4]} <[5]>=Z6 That is 1)<[0]>= {0} 2)<[1]>=<[5]>= Z6 3)<[2]>=<[4]>={[0],[2],[4]} 4)<[3]>={[0],[3]} so there's only 4 subgroups. 3)<[2]>=<[4]>={[0],[2],[4]} 4)<[3]>={[0],[3]} so there's only 4 subgroups.

Explanation / Answer

Yes everything looks correct, good job.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.