  The question of computing the group complexity of finite semigroups and
automata was first posed in K. Krohn and J. Rhodes, \textit{Complexity of
finite semigroups}, Annals of Mathematics (2) \textbf{88} (1968), 128--160,
motivated by the Prime Decomposition Theorem of K. Krohn and J. Rhodes,
\textit{Algebraic theory of machines, {I}: {P}rime decomposition theorem for
finite semigroups and machines}, Transactions of the American Mathematical
Society \textbf{116} (1965), 450--464. Here we provide an effective lower bound
for group complexity.
