Class preserving automorphisms of unitriangular groups

Abstract

Let ${\text{UT}}_n(K)$ be a unitriangular group over a field $K$ and ${\Gamma }_{n,k}:={\text{UT}}_n(K)/{\gamma }_k({\text{UT}}_n(K))$, where ${\gamma }_k({\mathrm{UT}}_n(K))$ denotes the $k$-th term of the lower central series of ${\mathrm{UT}}_n(K)$, $2\le k\le n$. We prove that the group of all class preserving automorphisms of ${\Gamma }_{n,k}$ is equal to $\Inn(Γ_{n,k})$ if and only if $K$ is a prime field. Let $G_n^{(m)}:={\mathrm{UT}}_n({\mathbb{F}}_{p^m})/{\gamma }_3({\mathrm{UT}}_n({\mathbb{F}}_{p^m}))$. We calculate the group of all class preserving automorphisms and class preserving outer automorphisms of $G_n^{(m)}$.

19 pages, accepted for publication in International Journal of Algebra and Computation

References in corpus (1)

• Class Preserving Automorphisms of Finite p-groups