Classifying Critical Points
1 hour ago
Wednesday, February 28, 2007
What the World Needs Now... is Algebra
While perusing my referrer tracker for this site, I've noticed in the last few days that a number of people are getting here by googling the phrase "Let G be a group of order 25. Prove that G is cyclic." Most of these are coming from either Bucknell or Iowa State. What is going on here? Do these people have an incredibly sadistic professor? Or have they fallen victim to a typo in some new algebra text? Any thoughts?
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2 comments:
Unfortunately, groups of order 25 are not necessarily cyclic. An example is provided by the subgroup generated by two cycles of order 5 in the symmetric group on 10 letters:
(1,2,3,4,5)and (6,7,8,9,10). It has order 25 but is not cyclic.
However, all groups of order 15 and 35 are cyclic. Maybe, just a misprint in the formulation of the problem?
"Unfortunately, groups of order 25 are not necessarily cyclic. "
Yes, that was the entire point of my posting this. :)
But clever idea about 15 or 35. I kinda secretly hope, though, that some prof got fed up with his students not paying any attention and assigned a problem that would clearly be false to anyone who had paid any attention, but would cause major headaches for everyone else.
Alternatively, the problem could have asked for a proof that the group is either cyclic or isomorphic to Z_5 x Z_5 and they may have figured that googling the first half would suffice. Unfortunately for them, googling anything along those lines often seems to lead only to this blog.
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