On unit group of finite semisimple group algebras of non-metabelian groups up to order 72

Gaurav Mittal; Rajendra Kumar Sharma

Mathematica Bohemica (2021)

  • Volume: 146, Issue: 4, page 429-455
  • ISSN: 0862-7959

Abstract

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We characterize the unit group of semisimple group algebras 𝔽 q G of some non-metabelian groups, where F q is a field with q = p k elements for p prime and a positive integer k . In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group ( ( C 3 × C 3 ) ⋊ C 3 ) ⋊ C 2 of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.

How to cite

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Mittal, Gaurav, and Sharma, Rajendra Kumar. "On unit group of finite semisimple group algebras of non-metabelian groups up to order 72." Mathematica Bohemica 146.4 (2021): 429-455. <http://eudml.org/doc/297419>.

@article{Mittal2021,
abstract = {We characterize the unit group of semisimple group algebras $\mathbb \{F\}_qG$ of some non-metabelian groups, where $F_q$ is a field with $q=p^k$ elements for $p$ prime and a positive integer $k$. In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group $((C_3\times C_3)\rtimes C_3)\rtimes C_2$ of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.},
author = {Mittal, Gaurav, Sharma, Rajendra Kumar},
journal = {Mathematica Bohemica},
keywords = {unit group; finite field; Wedderburn decomposition},
language = {eng},
number = {4},
pages = {429-455},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On unit group of finite semisimple group algebras of non-metabelian groups up to order 72},
url = {http://eudml.org/doc/297419},
volume = {146},
year = {2021},
}

TY - JOUR
AU - Mittal, Gaurav
AU - Sharma, Rajendra Kumar
TI - On unit group of finite semisimple group algebras of non-metabelian groups up to order 72
JO - Mathematica Bohemica
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 146
IS - 4
SP - 429
EP - 455
AB - We characterize the unit group of semisimple group algebras $\mathbb {F}_qG$ of some non-metabelian groups, where $F_q$ is a field with $q=p^k$ elements for $p$ prime and a positive integer $k$. In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group $((C_3\times C_3)\rtimes C_3)\rtimes C_2$ of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.
LA - eng
KW - unit group; finite field; Wedderburn decomposition
UR - http://eudml.org/doc/297419
ER -

References

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