Work

Word images and their impostors in finite nilpotent groups

Year: 2025

Type: article

Abstract: In 2014, Lubotzky showed that in a finite simple group G every automorphism invariant subset containing the identity is the image of a word map on G. We show that the number of such subsets in a finite nilpotent group may be arbitrarily larger than the number of word images. We construct a 2-exhaustive set of word maps on nilpotent groups of class 2 and demonstrate its minimality in some cases. We also find a sufficient condition, in terms of restrictions on word images, for a group to be a special p-group.

Source: International Journal of Algebra and Computation

DOI: 10.1142/s0218196725500171

Authors: Dilpreet Kaur, Harish Kishnani, Amit Kulshrestha

Institutions: Indian Institute of Technology Jodhpur, Indian Institute of Science Education and Research Mohali

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Department of Science and Technology, Ministry of Science and Technology, India, Ministry of Education, India

OpenAlex ID: W4410040264

FWCI:

Cites: 6

Cited by:

Related to: 10