The unit groups of semisimple group algebras of some non-metabelian groups of order 144

Gaurav Mittal; Rajendra K. Sharma

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 4, page 631-646
  • ISSN: 0862-7959

Abstract

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We consider all the non-metabelian groups G of order 144 that have exponent either 36 or 72 and deduce the unit group U ( 𝔽 q G ) of semisimple group algebra 𝔽 q G . Here, q denotes the power of a prime, i.e., q = p r for p prime and a positive integer r . Up to isomorphism, there are 6 groups of order 144 that have exponent either 36 or 72 . Additionally, we also discuss how to simply obtain the unit groups of the semisimple group algebras of those non-metabelian groups of order 144 that are a direct product of two nontrivial groups. In all, this paper covers the unit groups of semisimple group algebras of 17 non-metabelian groups.

How to cite

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Mittal, Gaurav, and Sharma, Rajendra K.. "The unit groups of semisimple group algebras of some non-metabelian groups of order $144$." Mathematica Bohemica 148.4 (2023): 631-646. <http://eudml.org/doc/299358>.

@article{Mittal2023,
abstract = {We consider all the non-metabelian groups $G$ of order $144$ that have exponent either $36$ or $72$ and deduce the unit group $U(\mathbb \{F\}_qG)$ of semisimple group algebra $\mathbb \{F\}_qG$. Here, $q$ denotes the power of a prime, i.e., $q=p^r$ for $p$ prime and a positive integer $r$. Up to isomorphism, there are $6$ groups of order $144$ that have exponent either $36$ or $72$. Additionally, we also discuss how to simply obtain the unit groups of the semisimple group algebras of those non-metabelian groups of order $144$ that are a direct product of two nontrivial groups. In all, this paper covers the unit groups of semisimple group algebras of $17$ non-metabelian groups.},
author = {Mittal, Gaurav, Sharma, Rajendra K.},
journal = {Mathematica Bohemica},
keywords = {unit group; finite field; Wedderburn decomposition},
language = {eng},
number = {4},
pages = {631-646},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The unit groups of semisimple group algebras of some non-metabelian groups of order $144$},
url = {http://eudml.org/doc/299358},
volume = {148},
year = {2023},
}

TY - JOUR
AU - Mittal, Gaurav
AU - Sharma, Rajendra K.
TI - The unit groups of semisimple group algebras of some non-metabelian groups of order $144$
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 4
SP - 631
EP - 646
AB - We consider all the non-metabelian groups $G$ of order $144$ that have exponent either $36$ or $72$ and deduce the unit group $U(\mathbb {F}_qG)$ of semisimple group algebra $\mathbb {F}_qG$. Here, $q$ denotes the power of a prime, i.e., $q=p^r$ for $p$ prime and a positive integer $r$. Up to isomorphism, there are $6$ groups of order $144$ that have exponent either $36$ or $72$. Additionally, we also discuss how to simply obtain the unit groups of the semisimple group algebras of those non-metabelian groups of order $144$ that are a direct product of two nontrivial groups. In all, this paper covers the unit groups of semisimple group algebras of $17$ non-metabelian groups.
LA - eng
KW - unit group; finite field; Wedderburn decomposition
UR - http://eudml.org/doc/299358
ER -

References

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