Question

find all subgroups of order 4 of z2×z4​

Answer 1

Answer:

There are eight subgroups of order 4 of z2×z4​

Explanation:

The only other subset that may conceivably be a subgroup of order 4 must be (0,0),(0,2),(1,0),(1,2) = Z2 2 > as there are three components of order 2: (0,2),(1,0),(1,2). This completes our list and is clearly a group. Consequently, Z2 Z4 has eight subgroups.

Subset :

If a subset H of a group G is a group under the operation in G, then H is a subgroup of G. The trivial subgroup is a subgroup of a group that only contains the identity element, e. The appropriate subgroup, denoted by H G, is a subgroup H of a group G that is a proper subset of G.

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