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Let $\mathcal{P}$ be an (unbounded) countable multiset of primes, let$G=\bigoplus_{p\in P}\mathbb{F}_p$. We study the $k$'th universalcharacteristic factors of an ergodic probability system $(X,\mathcal{B},\mu)$with respect to some measure preserving action of $G$. We find conditions underwhich every extension of these factors is generated by phase polynomials and wegive an example of an ergodic $G$-system that is not Abramov. In particular wegeneralize the main results of Bergelson Tao and Ziegler who proved a similartheorem in the special case $P=\{p,p,p,...\}$ for some fixed prime $p$. In asubsequent paper we use this result to prove a general structure theorem forergodic $\bigoplus_{p\in P}\mathbb{F}_p$-systems.

$\bigoplus_{p\in P}\mathbb{F}_p$-Systems as Abramov Systems