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math.GR2023
Fitting height and lengths of laws in finite solvable groups
Felix Leinen, Orazio Puglisi
Let G be a finite solvable group, and let h(G) denote its Fitting height, namely the length of a shortest normal series in G with nilpotent factors. We show, that any law in G has…
math.GR2018
A reduction theorem for nonsolvable finite groups
Francesco Fumagalli, Felix Leinen, Orazio Puglisi
Every finite group has a normal series each of whose factors is either a solvable group or a direct product of nonabelian simple groups. The minimum number of nonsolvable facto…
math.GR2011
Hirsch-Plotkin radical of stability groups
Carlo Casolo, Orazio Puglisi
We study the Hirsch-Plotkin radical of stability groups of (general) subspace series of infinite dimensional vector spaces. We show that in countable dimension and some other cases…