In the recent past, results have shown that Nilpotent groups such as p-groups, have normal series of finite length. Any finite p-group has many normal subgroups and consequently, the phenomenon of large number of non-isomorphic subgroups of a given order. This makes it an ideal object for combinatorial and cohomological investigations. Cartesian product (otherwise known as the product set) plays vital roles in the course of synthesizing the abstract groups. Previous studies have determined the number of distinct fuzzy subgroups of various finite p-groups including those of square-free order. However, not much work has been done on the fuzzy subgroup classification for the nilpotent groups formed from the Cartesian products of p-groups through their computations. Here, part of our intention is therefore trying to make some designs so as to classify the nilpotent groups formed from the Cartesian products of p-groups through their computations. The Cartesian products of p-groups were taken to obtain nilpotent groups. Results up to two dimensions are now obtainable. In this paper, the fuzzy subgroups of the nilpotent product of two abelian subgroups of orders 2n and 128. The integers n ≥ 7 have been successfully considered and the derivation for the explicit formulae for its number distinct fuzzy subgroups were calculated. Some methods were once being used in counting the chains of fuzzy subgroups of an arbitrary finite p-group G. Here, the adoption of the famous Inclusion-Exclusion principle is very necessary and imperative so as to obtain a reasonable, and as much as possible accurate.
| Published in | Mathematics and Computer Science (Volume 6, Issue 3) |
| DOI | 10.11648/j.mcs.20210603.11 |
| Page(s) | 45-48 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Finite p-Groups, Abelian Group, Fuzzy Subsets, Fuzzy Subgroups, Inclusion-Exclusion Principle, Maximal Subgroups, Nilpotent Group
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APA Style
Sunday Adesina Adebisi, Mike Ogiugo, Michael Enioluwafe. (2021). The Abelian Groups of Large Order: Perspective from (Fuzzy) Subgroups of Finite p-Groups. Mathematics and Computer Science, 6(3), 45-48. https://doi.org/10.11648/j.mcs.20210603.11
ACS Style
Sunday Adesina Adebisi; Mike Ogiugo; Michael Enioluwafe. The Abelian Groups of Large Order: Perspective from (Fuzzy) Subgroups of Finite p-Groups. Math. Comput. Sci. 2021, 6(3), 45-48. doi: 10.11648/j.mcs.20210603.11
AMA Style
Sunday Adesina Adebisi, Mike Ogiugo, Michael Enioluwafe. The Abelian Groups of Large Order: Perspective from (Fuzzy) Subgroups of Finite p-Groups. Math Comput Sci. 2021;6(3):45-48. doi: 10.11648/j.mcs.20210603.11
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Download@article{10.11648/j.mcs.20210603.11,
author = {Sunday Adesina Adebisi and Mike Ogiugo and Michael Enioluwafe},
title = {The Abelian Groups of Large Order: Perspective from (Fuzzy) Subgroups of Finite p-Groups},
journal = {Mathematics and Computer Science},
volume = {6},
number = {3},
pages = {45-48},
doi = {10.11648/j.mcs.20210603.11},
url = {https://doi.org/10.11648/j.mcs.20210603.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20210603.11},
abstract = {In the recent past, results have shown that Nilpotent groups such as p-groups, have normal series of finite length. Any finite p-group has many normal subgroups and consequently, the phenomenon of large number of non-isomorphic subgroups of a given order. This makes it an ideal object for combinatorial and cohomological investigations. Cartesian product (otherwise known as the product set) plays vital roles in the course of synthesizing the abstract groups. Previous studies have determined the number of distinct fuzzy subgroups of various finite p-groups including those of square-free order. However, not much work has been done on the fuzzy subgroup classification for the nilpotent groups formed from the Cartesian products of p-groups through their computations. Here, part of our intention is therefore trying to make some designs so as to classify the nilpotent groups formed from the Cartesian products of p-groups through their computations. The Cartesian products of p-groups were taken to obtain nilpotent groups. Results up to two dimensions are now obtainable. In this paper, the fuzzy subgroups of the nilpotent product of two abelian subgroups of orders 2n and 128. The integers n ≥ 7 have been successfully considered and the derivation for the explicit formulae for its number distinct fuzzy subgroups were calculated. Some methods were once being used in counting the chains of fuzzy subgroups of an arbitrary finite p-group G. Here, the adoption of the famous Inclusion-Exclusion principle is very necessary and imperative so as to obtain a reasonable, and as much as possible accurate.},
year = {2021}
}
TY - JOUR T1 - The Abelian Groups of Large Order: Perspective from (Fuzzy) Subgroups of Finite p-Groups AU - Sunday Adesina Adebisi AU - Mike Ogiugo AU - Michael Enioluwafe Y1 - 2021/06/07 PY - 2021 N1 - https://doi.org/10.11648/j.mcs.20210603.11 DO - 10.11648/j.mcs.20210603.11 T2 - Mathematics and Computer Science JF - Mathematics and Computer Science JO - Mathematics and Computer Science SP - 45 EP - 48 PB - Science Publishing Group SN - 2575-6028 UR - https://doi.org/10.11648/j.mcs.20210603.11 AB - In the recent past, results have shown that Nilpotent groups such as p-groups, have normal series of finite length. Any finite p-group has many normal subgroups and consequently, the phenomenon of large number of non-isomorphic subgroups of a given order. This makes it an ideal object for combinatorial and cohomological investigations. Cartesian product (otherwise known as the product set) plays vital roles in the course of synthesizing the abstract groups. Previous studies have determined the number of distinct fuzzy subgroups of various finite p-groups including those of square-free order. However, not much work has been done on the fuzzy subgroup classification for the nilpotent groups formed from the Cartesian products of p-groups through their computations. Here, part of our intention is therefore trying to make some designs so as to classify the nilpotent groups formed from the Cartesian products of p-groups through their computations. The Cartesian products of p-groups were taken to obtain nilpotent groups. Results up to two dimensions are now obtainable. In this paper, the fuzzy subgroups of the nilpotent product of two abelian subgroups of orders 2n and 128. The integers n ≥ 7 have been successfully considered and the derivation for the explicit formulae for its number distinct fuzzy subgroups were calculated. Some methods were once being used in counting the chains of fuzzy subgroups of an arbitrary finite p-group G. Here, the adoption of the famous Inclusion-Exclusion principle is very necessary and imperative so as to obtain a reasonable, and as much as possible accurate. VL - 6 IS - 3 ER -
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