IJPAM: Volume 116, No. 3 (2017)

Title

GROUPS WITH PRIMES ORDER CLASSES

Authors

Bilal N. Al-Hasanat$^1$, Mohanad N. Al-Hasanat$^2$, Asad A. Al-Hasanat$^3$
$^{1,2}$Al Hussein Bin Talal University
Ma'an, JORDAN
$^3$Yarmouk University
Irbid, JORDAN

Abstract

The order classes of finite groups can give certain and valuable properties of these groups. Unfortunately, not many research have illustrated these classes, it depends on many factors, such as the group description and the exponent of the group. In addition to the order of the group itself. Although, some of the previous research determined the order classes for certain groups, but the group structure has been used to show these classes. Conversely, in this paper we will configure the groups description using their order classes. This will introduce a new notion in finite groups called POC-group ``Primes Order Classes group''.

History

Received: 2017-05-23
Revised: 2017-06-03
Published: October 26, 2017

AMS Classification, Key Words

AMS Subject Classification: 20B05, 20E34
Key Words and Phrases: element order, order classes, prime order

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
Bilal Al-Hasanat, Ahmad, A. and Sulaiman, H. , The order classes ofdihedral groups. Proceeding of Mathematical Sciences NationalConference (SKSM21), AIP CONF PROC, 1605, No. 1 (2014),551-556, doi: https://doi.org/10.1063/1.4887648.

2
Bilal Al-Hasanat, Ahmad, A. and Sulaiman, H., Order classes ofsymmetric groups. International Journal of AppliedMathematics, 26, No. 4 (2013), 501-510, doi: https://doi.org/10.1155/2016/8435768.

3
Bilal Al-Hasanat, E. Al-Sarairah and Mahmoud Alhasanat, The orderclasses of 2-generator $p$-groups, Journal of AppliedMathematics (2017), to appear.

4
A.V. Vasilev, M.A. Grechkoseeva, V.D. Mazurov, Characterizationof the finite simple groups by spectrum and order, AlgebraLogic, 48 (2009), 385-409, doi: https://doi.org/10.1007/s10469-009-9074-9.

How to Cite?

DOI: 10.12732/ijpam.v116i3.15 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 3
Pages: 695 - 699


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).