Prove that an abelian group with two elements of order 2 must have a subgroup of order 4.
need help with my assignment.
this question is a bit hard, i need a liitle bit of help
2006-10-10 20:36:10 · 3 answers · asked by dsfdsfd f 1 in Science & Mathematics ➔ Mathematics
Let a and b be the two elements of order 2.
Then a^2 = e, and b^2 = e, but neither a nor b is equal to e, or they would not be of order 2.
Consider the set consisting of { a, b, ab, e }. You can show that this is a subgroup by showing that it's closed under multiplication.
The fact that the group is abelian is important because if it was not, then the set would have to include ba as well, in order to be closed, since it would be different from ab.
2006-10-10 20:41:48 · answer #1 · answered by James L 5 · 1⤊ 0⤋
drop the class
you're not ready for it ...
alternatively, quit web-surfing and study
2006-10-11 03:43:05 · answer #2 · answered by atheistforthebirthofjesus 6 · 0⤊ 0⤋
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2006-10-11 03:43:44 · answer #3 · answered by the great one 4 · 0⤊ 0⤋