  We study the influence of moderate exchange interactions of electrons on the
behavior of the peaks in the conductance of single electron transistors. We
numerically reproduce recently observed features of both the peak positions and
the peak heights magnetic field dependence. These features unambiguously
identify the total spin $S$ of each ground state. We evaluate the probability
of each $S$ (combination of spontaneous and induced magnetization) as a
function of the exchange strength, $J$, and external magnetic field, $B$. The
expressions involve only $J$ and $g$-factor as adjustable parameters. Moreover,
in a surprisingly broad parameter range these probabilities are determined by
certain linear combinations of $J$ and $B$.
