• SURJEET KOUR

Articles written in Proceedings – Mathematical Sciences

• On $n$-th class preserving automorphisms of $n$-isoclinism family

Let $G$ be a finite group and let $M$ and $N$ be two normal subgroups of $G$. Let $\rm{Aut}^{M}_{N}(G)$ denote the group of all automorphisms of $G$ which fix $N$ element-wise and act trivially on $G/M$. Let $n$ be a positive integer. In this article, we have shown that if $G$ and $H$ are two $n$-isoclinic groups, then there exists an isomorphism from $\rm{Aut}^{\gamma_{n+1}(G)}_{Z_{n} (G)} (G)$ to $\rm{Aut}^{\gamma_{ n+1}(H)}_{Z_{n} (H)} (H)$, which maps the group of $n$-th class preserving automorphisms of $G$ to the group of $n$-th class preserving automorphisms of $H$. Also, for a nilpotent group $G$ of class $(n + 1)$, if $\gamma_{n+1}(G)$ is cyclic, then we prove that $\rm{Aut}^{\gamma_{n+1}(G)}_{Z_{n} (G)} (G)$ is isomorphic to the group of inner automorphisms of a quotient group of $G$.

• On generalized cyclotomic derivations

In this article, we study the field of rational constants and Darboux polynomials of a generalized cyclotomic $K$-derivation $d$ of $K[X]$. It is shown that $d$ is without Darboux polynomials if and only if $K(X)^d = K$. The result is also studied in the tensor product of polynomial algebras.

• # Proceedings – Mathematical Sciences

Volume 133, 2023
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019