6 papers
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…
The Fitting height is bounded by a function of the exponent
Francesco Fumagalli, Felix Leinen, Orazio Puglisi
Every finite solvable group has a normal series with nilpotent factors. The smallest possible number of factors in such a series is called the Fitting height . In the pre…
An upper bound for the nonsolvable length of a finite group in terms of its shortest law
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 non-abelian simple groups. The minimum number of nonsolvable fact…
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…
Nil-automorphisms of groups with residual properties
Carlo Casolo, Orazio Puglisi
Following Plotkin we say that the automorphism of the group is a nil-automorphism if, for every , there exists such that . If the integer c…
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…