The Amit–Ashurst conjecture for finite metacyclic p-groups
(2023) In European Journal of Mathematics 9(3).- Abstract
The Amit conjecture about word maps on finite nilpotent groups has been shown to hold for certain classes of groups. The generalised Amit conjecture says that the probability of an element occurring in the image of a word map on a finite nilpotent group G is either 0, or at least 1/|G|. Noting the work of Ashurst, we name the generalised Amit conjecture the Amit–Ashurst conjecture and show that the Amit–Ashurst conjecture holds for finite p-groups with a cyclic maximal subgroup.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/274fa882-4eab-4bc6-8cb6-5ee40babbeda
- author
- Camina, Rachel D. ; Cocke, William L. and Thillaisundaram, Anitha LU
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Amit–Ashurst conjecture, Fibres of word maps, Metacyclic p-groups, Words
- in
- European Journal of Mathematics
- volume
- 9
- issue
- 3
- article number
- 46
- publisher
- Springer
- external identifiers
-
- scopus:85162023475
- ISSN
- 2199-675X
- DOI
- 10.1007/s40879-023-00644-x
- language
- English
- LU publication?
- yes
- id
- 274fa882-4eab-4bc6-8cb6-5ee40babbeda
- date added to LUP
- 2023-09-05 10:25:54
- date last changed
- 2023-09-05 10:25:54
@article{274fa882-4eab-4bc6-8cb6-5ee40babbeda,
abstract = {{<p>The Amit conjecture about word maps on finite nilpotent groups has been shown to hold for certain classes of groups. The generalised Amit conjecture says that the probability of an element occurring in the image of a word map on a finite nilpotent group G is either 0, or at least 1/|G|. Noting the work of Ashurst, we name the generalised Amit conjecture the Amit–Ashurst conjecture and show that the Amit–Ashurst conjecture holds for finite p-groups with a cyclic maximal subgroup.</p>}},
author = {{Camina, Rachel D. and Cocke, William L. and Thillaisundaram, Anitha}},
issn = {{2199-675X}},
keywords = {{Amit–Ashurst conjecture; Fibres of word maps; Metacyclic p-groups; Words}},
language = {{eng}},
number = {{3}},
publisher = {{Springer}},
series = {{European Journal of Mathematics}},
title = {{The Amit–Ashurst conjecture for finite metacyclic p-groups}},
url = {{http://dx.doi.org/10.1007/s40879-023-00644-x}},
doi = {{10.1007/s40879-023-00644-x}},
volume = {{9}},
year = {{2023}},
}