Maximal subgroups of finite soluble groups in general position

For a finite group G we investigate the difference between the maximum size MaxDim (G) of an “independent” family of maximal subgroups of G and maximum size m(G) of an irredundant sequence of generators of G. We prove that MaxDim (G) = m(G) if the derived subgroup of G is nilpotent. However, MaxDim (G) - m(G) can be arbitrarily large: for any odd prime p, we construct a finite soluble group with Fitting length two satisfying m(G) = 3 and MaxDim (G) = p. © 2015, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg.