G. Ercan

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20182026

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5 papers · 1 filter

math.GR2026

The Left-Nilpotent Residual and Its Supplements in Finite Skew Braces

Gülin Ercan, İsmail Ş. Güloğlu

Let $X$ be a finite skew brace, and let $L_{\infty} (X)$ be the final term of its left series. We introduce the left-nilpotent residual $\RL(X)$ and prove that $ \RL(X)=\Id_X\bigl(L_\…

math.GR2026

Ideals and Solvability in Skew Braces

Marco Damele, Gülin Ercan

We investigate how nilpotency assumptions on the multiplicative group of a finite skew brace constrain its ideal structure and solvability. Our first main result shows that, if \(B…

math.GR2026

Sylow theory and the nilpotency class of left nilpotent skew braces

Gülin Ercan, Şükran Gül, İsmail Ş. Güloğlu +1

Let $X$ be a finite left nilpotent skew brace and let $π$ be a set of primes. We show that every Hall $π$ -subgroup of the multiplicative group $(X, \cdot)$ is a Hall $π$ -subbrace of…

math.GR2026

The Baer Transform for Skew Braces

Gülin Ercan, Şükran Gül, İsmail Ş. Güloğlu +1

We introduce and study the Baer transform for finite skew braces whose additive group has odd order and nilpotency class at most $2$ . Starting from Baer's classical construction fo…

math.GR2026

Fixing size and Fitting height

İsmail Ş. Güloğlu, Gülin Ercan

Let $G$ be a finite solvable group on which a nilpotent group $A$ acts by automorphisms. The fixing size $c (G; A)$ of $A$ on $G$ is the number of $A$ -composition factors on…