28 citations · 91 across the 6 of their papers we have counts for
8 papers
Classification of Nottingham algebras
M. Avitabile, A. Caranti, S. Mattarei
The graded Lie algebra associated with the Nottingham group over a field of prime characteristic serves as a fundamental example of Nottingham algebras, a class of infinite-dimensi…
On Dedekind Skew Braces
A. Caranti, I. Del Corso, M. Di Matteo +2
Skew braces play a central role in the theory of set-theoretic non-degenerate solutions of the Yang--Baxter equation, since their algebraic properties significantly affect the beha…
On the Sylow Theorem for Skew Braces
A. Caranti, I. Del Corso, M. Di Matteo +2
We discuss the (first) Sylow theorem for certain classes of finite skew braces, proving it to hold true when the skew brace is two-sided, bi-skew, right nilpotent, -homomorphic…
Bi-Skew Braces and Regular Subgroups of the Holomorph
A. Caranti
L. Childs has defined a skew brace to be a bi-skew brace if is also a skew brace, and has given applications of this concept to the equivale…
Hopf-Galois structures on extensions of degree and skew braces of order : the cyclic Sylow -subgroup case
E. Campedel, A. Caranti, I. Del Corso
$\DeclareMathOperator{\Aut}{Aut}$Let be distinct primes, with . We classify the Hopf-Galois structures on Galois extensions of degree , such that the Sylow $…
The automorphism groups of groups of order
E. Campedel, A. Caranti, I. Del Corso
We record for reference a detailed description of the automorphism groups of the groups of order , where and are distinct primes.
Groups that have the same holomorph as a finite perfect group
A. Caranti, F. Dalla Volta
We describe the groups that have the same holomorph as a finite perfect group. Our results are complete for centerless groups. When the center is non-trivial, some questions remain…
The multiple holomorph of a finitely generated abelian group
A. Caranti, F. Dalla Volta
W.H.~Mills has determined, for a finitely generated abelian group , the regular subgroups of , the group of permutations on the set , which have the same ho…