On the isomorphism problem for modular group algebras of elementary abelian-by-cyclic p-groups

Czesław Bagiński

Colloquium Mathematicae (1999)

  • Volume: 82, Issue: 1, page 125-136
  • ISSN: 0010-1354

Abstract

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Let G be a finite p-group and let F be the field of p elements. It is shown that if G is elementary abelian-by-cyclic then the isomorphism type of G is determined by FG.

How to cite

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Bagiński, Czesław. "On the isomorphism problem for modular group algebras of elementary abelian-by-cyclic p-groups." Colloquium Mathematicae 82.1 (1999): 125-136. <http://eudml.org/doc/210745>.

@article{Bagiński1999,
abstract = {Let G be a finite p-group and let F be the field of p elements. It is shown that if G is elementary abelian-by-cyclic then the isomorphism type of G is determined by FG.},
author = {Bagiński, Czesław},
journal = {Colloquium Mathematicae},
keywords = {isomorphism problem; finite -groups; group rings; units},
language = {eng},
number = {1},
pages = {125-136},
title = {On the isomorphism problem for modular group algebras of elementary abelian-by-cyclic p-groups},
url = {http://eudml.org/doc/210745},
volume = {82},
year = {1999},
}

TY - JOUR
AU - Bagiński, Czesław
TI - On the isomorphism problem for modular group algebras of elementary abelian-by-cyclic p-groups
JO - Colloquium Mathematicae
PY - 1999
VL - 82
IS - 1
SP - 125
EP - 136
AB - Let G be a finite p-group and let F be the field of p elements. It is shown that if G is elementary abelian-by-cyclic then the isomorphism type of G is determined by FG.
LA - eng
KW - isomorphism problem; finite -groups; group rings; units
UR - http://eudml.org/doc/210745
ER -

References

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  1. [1] C. Bagiński, The isomorphism question for modular group algebras of metacyclic p-groups, Proc. Amer. Math. Soc. 104 (1988), 39-42. Zbl0663.20006
  2. [2] C. Bagiński and A. Caranti, The modular group algebras of p-groups of maximal class, Canad. J. Math. 40 (1988), 1422-1435. Zbl0665.20003
  3. [3] B. Huppert, Endliche Gruppen I, Springer, Berlin, 1983. Zbl0217.07201
  4. [4] R. Sandling, Units in the modular group algebra of a finite abelian p-group, J. Pure Appl. Algebra 33 (1984), 337-346. Zbl0543.20008
  5. [5] R. Sandling, The isomorphism problem for group rings: A survey, in: Lecture Notes in Math. 1142, Springer, Berlin, 1985, 256-288. 
  6. [6] R. Sandling, The modular group algebra of a central-elementary-by-abelian p-group, Arch. Math. (Basel) 52 (1989), 22-27. Zbl0632.16011
  7. [7] R. Sandling, The modular group algebra problem for small p-groups of maximal class, Canad. J. Math. 48 (1996), 1064-1078. Zbl0863.20003
  8. [8] S. Sehgal, Topics in Group Rings, Pure Appl. Math. 50, Marcel Dekker, New York, 1978. 
  9. [9] U. H. M. Webb, An elementary proof of Gaschütz' theorem, Arch. Math. (Basel) 35 (1980), 23-26. Zbl0423.20022
  10. [10] M. Wursthorn, Isomorphism of modular group algebras: An algorithm and its application to groups of order 2 6 , J. Symbolic Comput. 15 (1993), 211-227. Zbl0782.20001

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