LCD codes and self-orthogonal codes in generalized dihedral group algebras

This paper proves that the infinite dihedral group is only such a free product of two finite groups that its group algebra over a field [Formula: see text] is a CS-ring in case the orders of two groups are not zero in [Formula: see text]. Furthermore, it is shown that the group algebra of any free product of two finite cyclic groups does not satisfy the condition [Formula: see text].

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The unit group of finite group algebra of a generalized dihedral group

Asian-European Journal of Mathematics ◽

10.1142/s179355711450034x ◽

2014 ◽

Vol 07 (02) ◽

pp. 1450034 ◽

Cited By ~ 1

Author(s):

Neha Makhijani ◽

R. K. Sharma ◽

J. B. Srivastava

Keyword(s):

Finite Group ◽

Group Theory ◽

Finite Field ◽

Group Algebra ◽

Dihedral Group ◽

Unit Group ◽

Generalized Dihedral Group

Let [Formula: see text] be a generalized dihedral group of order 2n and 𝔽q be a finite field having q elements. In this note, we establish the structure of the unit group of [Formula: see text] for any odd n ≥ 3. This extends a result due to Kaur and Khan [Units in 𝔽2D2p, J. Algebra Appl. 13(2) (2014) 9pp., doi: 10.1142/S0219498813500904] as well as a result due to the authors [Units in 𝔽2kD2n, Int. J. Group Theory 3(3) (2014) 25–34].

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Nowhere-zero 3-flows in Cayley graphs on generalized dihedral group and generalized quaternion group

Frontiers of Mathematics in China ◽

10.1007/s11464-014-0378-2 ◽

2014 ◽

Vol 10 (2) ◽

pp. 293-302

Author(s):

Liangchen Li ◽

Xiangwen Li

Keyword(s):

Dihedral Group ◽

Cayley Graphs ◽

Quaternion Group ◽

Generalized Quaternion Group ◽

Generalized Quaternion ◽

Generalized Dihedral Group

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Derivations of Group Algebras of the Infinite Dihedral Group

Groups - Korea 94 ◽

10.1515/9783110908978.163 ◽

2012 ◽

Author(s):

Naoki Kawamoto

Keyword(s):

Dihedral Group ◽

Group Algebras

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On Minimal Distance-Regular Cayley Graphs of Generalized Dihedral Groups

The Electronic Journal of Combinatorics ◽

10.37236/9755 ◽

2020 ◽

Vol 27 (4) ◽

Author(s):

Štefko Miklavič ◽

Primož Šparl

Keyword(s):

Closed Subset ◽

Dihedral Group ◽

Cayley Graphs ◽

Complete Classification ◽

Minimal Distance ◽

Dihedral Groups ◽

Generalized Dihedral Group

Let $G$ denote a finite generalized dihedral group with identity $1$ and let $S$ denote an inverse-closed subset of $G \setminus \{1\}$, which generates $G$ and for which there exists $s \in S$, such that $\langle S \setminus \{s,s^{-1}\} \rangle \ne G$. In this paper we obtain the complete classification of distance-regular Cayley graphs $\mathrm{Cay}(G;S)$ for such pairs of $G$ and $S$.

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