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A POLYNOMIAL APPROACH TO COCYCLES OVER ELEMENTARY ABELIAN GROUPS

Published online by Cambridge University Press:  01 October 2008

D. G. FARMER
Affiliation:
RMIT University, Melbourne, VIC 3001, Australia (email: [email protected])
K. J. HORADAM*
Affiliation:
RMIT University, Melbourne, VIC 3001, Australia (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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We derive bivariate polynomial formulae for cocycles and coboundaries in Z2(ℤpn,ℤpn), and a basis for the (pn−1−n)-dimensional GF(pn)-space of coboundaries. When p=2 we determine a basis for the -dimensional GF(2n)-space of cocycles and show that each cocycle has a unique decomposition as a direct sum of a coboundary and a multiplicative cocycle of restricted form.

Type
Research Article
Copyright
Copyright © 2008 Australian Mathematical Society

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