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ALMOST ABELIAN NUMBERS

Part of: Representation theory of groups

Published online by Cambridge University Press:  20 December 2024

IUILA-CĂTĂLINA PLEŞCA Open the ORCID record for IUILA-CĂTĂLINA PLEŞCA [Opens in a new window]  and
MARIUS TĂRNĂUCEANU Open the ORCID record for MARIUS TĂRNĂUCEANU [Opens in a new window]
IUILA-CĂTĂLINA PLEŞCA*
Affiliation:
Faculty of Mathematics, ‘Al. I. Cuza’ University of Iaşi, Iaşi, Romania
MARIUS TĂRNĂUCEANU
Affiliation:
Faculty of Mathematics, ‘Al. I. Cuza’ University of Iaşi, Iaşi, Romania e-mail: tarnauc@uaic.ro
*
e-mail: dankemath@yahoo.com
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Abstract

We introduce the concept of almost $\mathcal {P}$-numbers where $\mathcal {P}$ is a class of groups. We survey the existing results in the literature for almost cyclic numbers, and give characterisations for almost abelian and almost nilpotent numbers proving these two concepts are equivalent.

Keywords

finite groupsnilpotent groupsabelian groups

MSC classification

Primary: 20D05: Finite simple groups and their classification
Secondary: 20D40: Products of subgroups

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 111 , Issue 3 , June 2025 , pp. 518 - 523
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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References

Binjedaen, H. I., ‘When there is a unique group of a given order and related results’, Graduate Thesis, Missouri State University, 2016. https://bearworks.missouristate.edu/theses/2952/.Google Scholar
Campedel, E., Caranti, A. and Del Corso, I., ‘The automorphism groups of groups of order ${p}^2q$ ’, Int. J. Group Theory 10(3) (2021), 149–157.Google Scholar
Isaacs, I. M., Finite Group Theory (American Mathematical Society, Providence, RI, 2008).Google Scholar
Pakianathan, J. and Shankar, K., ‘Nilpotent numbers’, Amer. Math. Monthly 107(7) (2000), 631–634.CrossRefGoogle Scholar