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Dergiler / Journal of Algebra Combinatorics Discrete Structures and Applications / 2022 / Cilt: 9 - Sayı: 2

On the isomorphism of unitary subgroups of noncommutative group algebras

Zsolt Adam BALOGH
Sayfa
45–51
Yayın Tarihi
2022-05-13
DOI
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In this paper we present a non-abelian pp-group GG whose group algebra FGFG has sharply less number of non-isomorphic *\cd-unitary subgroups than the given upper bound.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let FGFG be the group algebra of a finite pp-group GG over a field FF of characteristic pp.
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Temel Bulgular & Veri:Let *\cd be an involution of the group algebra FGFG which arises form the group basis GG.
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Sonuç & Katkı:In this paper we present a non-abelian pp-group GG whose group algebra FGFG has sharply less number of non-isomorphic *\cd-unitary subgroups than the given upper bound.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Group ring · Group of units · Unitary subgroup

Abstract

Let FGFG be the group algebra of a finite pp-group GG over a field FF of characteristic pp. Let *\cd be an involution of the group algebra FGFG which arises form the group basis GG. The upper bound for the number of non-isomorphic *\cd-unitary subgroups is the number of conjugacy classes of the automorphism group GG with all the elements of order two. The upper bound is not always reached in the case when GG is an abelian group, but for non-abelian case the question is open. In this paper we present a non-abelian pp-group GG whose group algebra FGFG has sharply less number of non-isomorphic *\cd-unitary subgroups than the given upper bound.

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Bu Makaleye Atıf Yap

BALOGH, Z. A. (2022). On the isomorphism of unitary subgroups of noncommutative group algebras. Journal of Algebra Combinatorics Discrete Structures and Applications, Cilt: 9 - Sayı: 2, 45–51. https://ajindex.com/articles/861488

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Kaynakça (19)

  1. Z. Balogh, On unitary subgroups of group algebras, Int. Electron. J. Algebra 29(29) (2021) 187–198
  2. Z. Balogh, V. Bovdi, The isomorphism problem of unitary subgroups of modular group algebras, Publ. Math. Debrecen 97(1-2) (2020) 27–39
  3. Z. Balogh, L. Creedon, J. Gildea, Involutions and unitary subgroups in group algebras, Acta Sci. Math. (Szeged) 79(3-4) (2013) 391–400
  4. Z. Balogh, V. Laver. Unitary subgroups of commutative group algebras of characteristic 2. Ukraïn. Mat. Zh. 72(6) (2020) 751–757
  5. A. Bovdi, L. Erdei, Unitary units in modular group algebras of groups of order 16, Tech. Rep., Univ. Debrecen, L. Kossuth Univ. 4(157) (1996) 1–16
  6. A. Bovdi, L. Erdei. Unitary units in modular group algebras of 2-groups. Comm. Algebra 28(2) (2000) 625–630
  7. A. Bovdi, P. Lakatos, On the exponent of the group of normalized units of modular group algebras, Publ. Math. Debrecen 42(3-4) (1993) 409–415
  8. A. Bovdi, A. Szakács, Units of commutative group algebra with involution, Publ. Math. Debrecen 69(3) (2006) 291–296
  9. A. A. Bovdi, Unitarity of the multiplicative group of an integral group ring, Mat. Sb. (N.S.) 47(2) (1984) 377–389
  10. A. A. Bovdi, A. A. Sakach, Unitary subgroup of the multiplicative group of a modular group algebra of a finite abelian p-group. Mat. Zametki 45(6) (1989) 445–450
  11. A. A. Bovdi, A.Szakács, A basis for the unitary subgroup of the group of units in a finite commutative group algebra, Publ. Math. Debrecen 46(1-2) (1995) 97–120
  12. V. Bovdi, L. G. Kovács, Unitary units in modular group algebras, Manuscripta Math. 84(1) (1994) 57–72
  13. V. Bovdi, A. L. Rosa, On the order of the unitary subgroup of a modular group algebra, Comm. Algebra 28(4) (2000) 1897–1905
  14. V. Bovdi, M. Salim, On the unit group of a commutative group ring, Acta Sci. Math. (Szeged) 80(3-4) (2014) 433–445
  15. V. A. Bovdi, A. N. Grishkov, Unitary and symmetric units of a commutative group algebra, Proc. Edinb. Math. Soc. 62(3) (2019) 641–654
  16. L. Creedon, J. Gildea, Unitary units of the group algebra $F_{2^k}D_8$, Internat. J. Algebra Comput. 19(2) (2009) 283–286
  17. L. Creedon, J. Gildea, The structure of the unit group of the group algebra$F_{2^k}D_8$, Canad. Math. Bull. 54(2) (2011) 237–243
  18. J. Gildea, The structure of the unitary units of the group algebra $F_{2^k}D_8$, Int. Electron. J. Algebra 9 (2011) 171–176
  19. D. W. Lewis. Involutions and anti-automorphisms of algebras, Bull. London Math. Soc. 38(4) (2006)