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lapo4ka [179]
3 years ago
13

An example of an abelian group which is not cyclic

Mathematics
1 answer:
Leokris [45]3 years ago
7 0

G=Z6×Z2G=Z6×Z2 will do (where ZnZn denotes the cyclic group of order nn). As a direct product of cyclic (so abelian) groups, GG is again abelian. Given any element (x,y)∈G(x,y)∈G, the order of (x,y)(x,y) will be the least common multiple of the orders of x,y.x,y.  

The order of xx must divide 66 and the order of yy must divide 2,2, so the order of (x,y)(x,y) is at most lcm(6,2)=6.lcm⁡(6,2)=6. But |G|=|Z6|⋅|Z2|=6⋅2=12.|G|=|Z6|⋅|Z2|=6⋅2=12. Since no element of GG has order 12,12, then GG is not cyclic.

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Ad libitum [116K]

The area of the composite figure can be found by summing the whole area that made up the figure. Therefore, the area of the figure is 213.5m²

<h3>Area of a composite figure</h3>

The area of the composite figure is the sum of the area of the whole figure.

Therefore, the composite figure can be divided into 2 triangles and two rectangles.

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learn more on area here: brainly.com/question/27744042

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