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

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