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+--- Thread: Tommy groups (/showthread.php?tid=1002)
Tommy groups - tommy1729 - 05/14/2015
Im very intrested in abelian gaussian Groups. I call them Tommy groups.
Beware this is not to be confused with the usual gaussian groups.
The terminology is made Up.
Basically its just the gaussian integers mod p for some prime p that satisfy Some conditions.
Or equivalent the group Z_p[i] or the ring Z mod p extended with i.
To avoid zero-divisors and make i meaningful we take p such that
X^2 = -1 mod p has no solution.
Or equivalent p =/= a^2 + b^2.
Additional conditions are considered.
And are part of the debate/theory.
Lots of number theory,ring- and group theory come together here.
X^i is a subject.
This has meaning if x^2 = -1 mod (p-1) has a solution.
Variants of fermat little and flt are also a topic.
Imho this kind of math is left too soon.
Some people say this is below their or my level , but i disagree.
Just like tetration this deserves a second look.
Thought you might wanted to know.
Regards
Tommy1729
RE: Tommy groups - tommy1729 - 05/15/2015
X^{p^2}
Something to think about.
Regards
Tommy1729