arXiv subjects

Martina Iannaccone

Publications and source records attributed to Martina Iannaccone.

2 recordsLinked to original sources

arXiv2026

Near-Rings and Skew Braces

This paper adapts Rump's correspondence between radical rings and braces to a more general setting, utilizing a suitable class of near-rings. Given a right near-ring $(R,+,\circ)$ with a multiplicative identity, we define a new operation that yields a monoid. Under natural compatibility conditions expressed via a filtration, this monoid becomes a topological group, yielding a topological right skew brace. This generalization recovers radical-ring braces and successfully applies to near-rings of maps under composition. We provide several explicit applications, demonstrating that the Nottingham group, groups of triangular functions, iterated wreath products of arbitrary groups, and groups of IA-automorphisms of free nilpotent groups naturally arise as multiplicative groups of such topological skew braces.

math.GR↗

arXiv2026

On Zappa--Szép products of a wreathed $2$-group and a cyclic group

Let $n, m \ge 1$, and let $H = C_{2^n}\wr C_2$ be the wreathed $2$-group and $K = C_{2^m}=\langle z \rangle$ a cyclic group. We classify the Zappa--Szép products $G = HK$ in which the base $B \cong C_{2^n}\times C_{2^n}$ of $H$ is normal in $G$. When the matrix $Z$ of the $z$-action on $B$ commutes with the swap $J$ of the two base generators -- equivalently, $Z$ is symmetric circulant -- we classify these products by an explicit system of seven polynomial congruences in a tuple $(p,q,r,s,c)$. Dropping this hypothesis, we obtain a unified classification of all such products with $B$ normal by five congruences on the entries of $Z$ and the parameters $(r,s,c)$, of which the symmetric case is the specialisation $JZ = ZJ$. Finally, we separately treat the classification for the modulus $M = 2^m = 4$, since in this case the congruences degenerate.

math.GR↗