Re: A funny quote on a problem in Abstract Algebra (was it in Herstein's "Topics in Algebra"?)

On Sat, 28 Jul 2007 17:34:48 GMT, Michael Press
<rubrum@xxxxxxxxxxx> wrote:

In article
<vfoja31jgkss8utjlhaq2hghmde63nui48@xxxxxxx>,
Angus Rodgers <twirlip@xxxxxxxxxxx> wrote:

I think you are probably remembering the parenthetical
remark which was added to Problem 2.5.26 on page 48 of
the second edition:

"Don't be discouraged if you don't get this problem
with what you know of group theory up to this stage.
I don't know anybody, including myself, who has done
it subject to the restriction of using material
developed so far in the text. But it is fun to try.
I've had more correspondence about this problem than
about any other point in the whole book."

(I must admit I haven't even started reading Herstein
yet, but I skimmed over it recently and noticed this.)

Therefore the problem appears in the first edition,
which is the only one at hand to me presently. Problem
2.5.26 does not exist in the first edition. Section 2.5
covers normal subgroups and quotient groups. So the
question: what is the problem?

"If an abelian group has subgroups of orders m and n,
respectively, then show it has a subgroup whose order
is the least common multiple of m and n."

(It's in the section entitled "A Counting Principle".)
--
Angus Rodgers
(twirlip@ eats spam; reply to angusrod@)
Contains mild peril
.

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