Re: Bilinear Paaring and groups

Hi,

Not generally. For example, if G_1 and G_2 are two elementary abelian
groups of order p^2, then you can define a non-degenerate pairing
which is onto an elementary abelian group of order p^4 by taking the
2-nilpotent product of G1 and G2, and using the commutator bracket to
define the pairing.

What properties are you requiring your bilinear pairing to have? What
properties do you require of G_1 and G_2? Is there anything special
about q (prime? power of a prime? anything?)
G_1 and G_2 are of prime order q. Is there any big difference, whether I choose G_1 to be additive or multiplicative?

Thanks in advance,
Zsuzsi
.

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