A group G has exactly 8 elements or order 3

nowimpsbball

How many subgroups of order 3 does G have?

So we have 8 elements, its prime decomposition is 8=2^3. The number of different ways to get factors is how many subgroups, at least that is what I interpret from my notes...so there are 2^3, 2*2^2, and 2*2*2, so three different ways to get factors, am I doing this right?

Thanks

d_leet

Do you mean G has 8 elements OR order 3, or do you mean G has 8 elements OF order 3.

nowimpsbball

Quote by d_leet

Do you mean G has 8 elements OR order 3, or do you mean G has 8 elements OF order 3.

g has 8 elements OF order 3, my bad

mathwonk

every subgroup of order three has how many elements of order three?

and how many common elements of order three do two distinct subgroups of order three have?

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nowimpsbball	A group G has exactly 8 elements or order 3 How many subgroups of order 3 does G have? So we have 8 elements, its prime decomposition is 8=2^3. The number of different ways to get factors is how many subgroups, at least that is what I interpret from my notes...so there are 2^3, 22^2, and 22*2, so three different ways to get factors, am I doing this right? Thanks

d_leet	Do you mean G has 8 elements OR order 3, or do you mean G has 8 elements OF order 3.

mathwonk Recognitions: Homework Help Science Advisor	A group G has exactly 8 elements or order 3 every subgroup of order three has how many elements of order three? and how many common elements of order three do two distinct subgroups of order three have?