Structure of the unit group of the group algebras of non-metabelian groups of order 128

Navamanirajan Abhilash; Elumalai Nandakumar; Rajendra K. Sharma; Gaurav Mittal

Mathematica Bohemica (2025)

  • Issue: 1, page 1-23
  • ISSN: 0862-7959

Abstract

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We characterize the unit group for the group algebras of non-metabelian groups of order 128 over the finite fields whose characteristic does not divide the order of the group. Up to isomorphism, there are 2328 groups of order 128 and only 14 of them are non-metabelian. We determine the Wedderburn decomposition of the group algebras of these non-metabelian groups and subsequently characterize their unit groups.

How to cite

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Abhilash, Navamanirajan, et al. "Structure of the unit group of the group algebras of non-metabelian groups of order 128." Mathematica Bohemica (2025): 1-23. <http://eudml.org/doc/299898>.

@article{Abhilash2025,
abstract = {We characterize the unit group for the group algebras of non-metabelian groups of order 128 over the finite fields whose characteristic does not divide the order of the group. Up to isomorphism, there are 2328 groups of order 128 and only 14 of them are non-metabelian. We determine the Wedderburn decomposition of the group algebras of these non-metabelian groups and subsequently characterize their unit groups.},
author = {Abhilash, Navamanirajan, Nandakumar, Elumalai, Sharma, Rajendra K., Mittal, Gaurav},
journal = {Mathematica Bohemica},
keywords = {non-metabelian groups; finite field; group algebra; unit group},
language = {eng},
number = {1},
pages = {1-23},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Structure of the unit group of the group algebras of non-metabelian groups of order 128},
url = {http://eudml.org/doc/299898},
year = {2025},
}

TY - JOUR
AU - Abhilash, Navamanirajan
AU - Nandakumar, Elumalai
AU - Sharma, Rajendra K.
AU - Mittal, Gaurav
TI - Structure of the unit group of the group algebras of non-metabelian groups of order 128
JO - Mathematica Bohemica
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 1
EP - 23
AB - We characterize the unit group for the group algebras of non-metabelian groups of order 128 over the finite fields whose characteristic does not divide the order of the group. Up to isomorphism, there are 2328 groups of order 128 and only 14 of them are non-metabelian. We determine the Wedderburn decomposition of the group algebras of these non-metabelian groups and subsequently characterize their unit groups.
LA - eng
KW - non-metabelian groups; finite field; group algebra; unit group
UR - http://eudml.org/doc/299898
ER -

References

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