Self-Dual Group Codes in Finite Dihedral Group Algebra

2020 ◽  
Vol 24 (9) ◽  
pp. 1894-1898
Author(s):  
Yanyan Gao ◽  
Qin Yue ◽  
Xinmei Huang
Keyword(s):  
Group Algebra ◽  
Dihedral Group ◽  
Dual Group ◽  
Group Codes

On the order of unitary subgroup of the modular group algebra 𝔽2kD2N

2015 ◽  
Vol 14 (08) ◽  
pp. 1550129 ◽  
Author(s):  
Neha Makhijani ◽  
R. K. Sharma ◽  
J. B. Srivastava
Keyword(s):  
Group Algebra ◽  
Modular Group ◽  
Dihedral Group ◽  
Group Of Units ◽  
Modular Group Algebra ◽  
Canonical Involution ◽  
Unitary Subgroup

Let 𝔽qD2N be the group algebra of D2N, the dihedral group of order 2N, over 𝔽q = GF (q). In this paper, we compute the order of the unitary subgroup of the group of units of 𝔽2kD2N with respect to the canonical involution ∗.

scholarly journals UNITS IN F2D2p

2013 ◽  
Vol 13 (02) ◽  
pp. 1350090 ◽  
Author(s):  
KULDEEP KAUR ◽  
MANJU KHAN
Keyword(s):  
Finite Field ◽  
Group Algebra ◽  
Dihedral Group ◽  
Unit Group ◽  
Normal Subgroups ◽  
Canonical Involution ◽  
Unitary Subgroup ◽  
Bicyclic Units

Let p be an odd prime, D2p be the dihedral group of order 2p, and F2 be the finite field with two elements. If * denotes the canonical involution of the group algebra F2D2p, then bicyclic units are unitary units. In this note, we investigate the structure of the group [Formula: see text], generated by the bicyclic units of the group algebra F2D2p. Further, we obtain the structure of the unit group [Formula: see text] and the unitary subgroup [Formula: see text], and we prove that both [Formula: see text] and [Formula: see text] are normal subgroups of [Formula: see text].

scholarly journals Codes in a Dihedral Group Algebra

2019 ◽  
Vol 53 (7) ◽  
pp. 745-754
Author(s):  
K. V. Vedenev ◽  
V. M. Deundyak
Keyword(s):  
Group Algebra ◽  
Dihedral Group

The Structure of the Unit Group of the Group Algebra

2011 ◽  
Vol 54 (2) ◽  
pp. 237-243 ◽  
Author(s):  
Leo Creedon ◽  
Joe Gildea
Keyword(s):  
Finite Field ◽  
Group Ring ◽  
Group Algebra ◽  
Dihedral Group ◽  
Unit Group ◽  
Cyclic Groups ◽  
Split Extensions

AbstractLet RG denote the group ring of the group G over the ring R. Using an isomorphism between RG and a certain ring of n×n matrices in conjunction with other techniques, the structure of the unit group of the group algebra of the dihedral group of order 8 over any finite field of chracteristic 2 is determined in terms of split extensions of cyclic groups.

scholarly journals On the structure of a real crossed group algebra

1988 ◽  
Vol 38 (1) ◽  
pp. 31-40 ◽  
Author(s):  
K. Buzási
Keyword(s):  
Group Algebra ◽  
Dihedral Group ◽  
Matrix Algebras ◽  
Generating Sets ◽  
Zero Divisors ◽  
Finite Set ◽  
Representations Of Finite Groups ◽  
New Ideas ◽  
Real Quaternions ◽  
Torsion Free

The main result of this paper is that there exist non-principal left ideals in a certain twisted group algebra A of the infinite dihedral group ≤ a, b | b−1ab = a−1, b2 = 1 ≥ over the field R of real numbers: namely in the A defined by b−l ab = a−1, b2 = −1, and λa = aλ, λb = bλ for all real λ.The motivation comes from the study (in a series of papers by Berman and the author) of finitely generated torsion-free RG-modules for groups G which have an infinite cyclic subgroup of finite index. In a sense, this amounts to studying modules over (full matrix algebras over) a finite set of R-algebras [namely, for the groups in question, these algebras take on the role played by R, C and H (the real quaternions) in the theory of real representations of finite groups]. For all but two algebras in that finite set, satisfying results have been obtained by exploiting the fact that each of them is either a ring with zero divisors or a principal left ideal ring. The other two are known to have no zero divisors. One of them is the present A. The point of the main result is that new ideas will be needed for understanding A-modules.A number of subsidiary results are concerned with convenient generating sets for left ideals in A.

A note on self-dual group codes

2002 ◽  
Vol 48 (12) ◽  
pp. 3107-3109 ◽  
Author(s):  
W. Willems
Keyword(s):  
Dual Group ◽  
Group Codes
Sign in / Sign up

Export Citation Format

Share Document