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Enhanced power graphs of finite groups with cograph structure
Daniela Bubboloni, Francesco Fumagalli, Cheryl E. Praeger
The enhanced power graph, , of a group has vertex set and two elements are adjacent if they generate a cyclic subgroup. In the case of finite groups, we ide…
On the Gowers trick for classical simple groups
Francesco Fumagalli, Attila Maróti
If , , are subsets in a finite simple group of Lie type at least two of which are normal with relatively large, then we establish a stronger conclusion th…
On some questions related to integrable groups
Russell Blyth, Francesco Fumagalli, Francesco Matucci
A group is integrable if it is isomorphic to the derived subgroup of a group ; that is, if , and in this case is an integral of . If is a subgroup of…
On the maximal number of elements pairwise generating the finite alternating group
Francesco Fumagalli, Martino Garonzi, Pietro Gheri
Let be the alternating group of degree . Let be the maximal size of a subset of such that whenever and and le…
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…