Question

Find all the subgroups of each of the groups: Z4, Z7, Z12, D4 and D5.

Answer 1

Zn is cyclic group ... So every divisor of n will gives a subgroup of Zn.... Like for Z4.... Divisor of 4 are 1,2,4

And subgroup of cycle group are cyclic . So subgroup of Z4 are

Identify subgroup, Z2, Z4...

For Z7 as 7 us prime so divisor of 7 are 1 and 7

Only subgroup are identity and the Z7 itself.

For Z12, ... Identity Z2, Z3, Z4, Z6, Z12

For Dn..... Have you know the structure of this group??

Let me give some ..