Re: The quaternion group as a product

In article <14780592.1211173000176.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
Adam Burley <ajburley@xxxxxxxxxxxxxx> wrote:
Is there a known product corresponding to this
situation?

The product of subgroups. If either H or K is normal
and maximal, then
G = HK provided H and K are distinct, but the
condition is far from
necessary.

Again, PLEASE hit the carriage return when you get to about 65-70
characters. DO NOT rely on Mathforum's editor to break up your lines:
it doesn't do it properly. Your reply was one long line that ran off
the right edge of my screen.

I am familiar with this product of subgroups, it being the underlying
idea behind the internal direct/semidirect product.

No, it is not. Because nowhere was there a requirement that H and K
intersect trivially.

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org

.

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