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A group G has exactly 8 elements or order 3

by nowimpsbball
Tags: elements, order
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nowimpsbball
#1
Jan30-08, 02:54 PM
P: 15
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
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d_leet
#2
Jan30-08, 05:00 PM
P: 1,075
Do you mean G has 8 elements OR order 3, or do you mean G has 8 elements OF order 3.
nowimpsbball
#3
Jan30-08, 05:16 PM
P: 15
Quote Quote by d_leet View Post
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
#4
Jan31-08, 02:06 AM
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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?


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