scholarly journals On the extendability of Bi-Cayley graphs of finite abelian groups

2009 ◽  
Vol 309 (20) ◽  
pp. 5943-5949 ◽  
Author(s):  
Yanfeng Luo ◽  
Xing Gao
Keyword(s):  
Abelian Groups ◽  
Cayley Graphs ◽  
Finite Abelian Groups

scholarly journals On the extendability of certain semi-Cayley graphs of finite abelian groups

2011 ◽  
Vol 311 (17) ◽  
pp. 1978-1987 ◽  
Author(s):  
Xing Gao ◽  
Wenwen Liu ◽  
Yanfeng Luo
Keyword(s):  
Abelian Groups ◽  
Cayley Graphs ◽  
Finite Abelian Groups

scholarly journals Integral Sets and Cayley Graphs of Finite Groups

10.37236/2053 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Roger C. Alperin ◽  
Brian L. Peterson
Keyword(s):  
Boolean Algebra ◽  
Finite Groups ◽  
Dihedral Group ◽  
Abelian Groups ◽  
Cayley Graphs ◽  
Finite Abelian Groups

Integral sets of finite groups are discussed and related to the integral Cayley graphs. The Boolean algebra of integral sets are determined for dihedral group and finite abelian groups. We characterize the finite abelian groups as those finite groups where the Boolean algebra generated by  integral sets equals  the Boolean algebra generated by its subgroups.

scholarly journals Integral Quartic Cayley Graphs on Abelian Groups

10.37236/576 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
A. Abdollahi ◽  
E. Vatandoost
Keyword(s):  
Abelian Groups ◽  
Cayley Graphs ◽  
Finite Abelian Groups ◽  
Side Result

A graph is called integral, if its adjacency eigenvalues are integers. In this paper we determine integral quartic Cayley graphs on finite abelian groups. As a side result we show that there are exactly $27$ connected integral Cayley graphs up to $11$ vertices.

scholarly journals EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES
Keyword(s):  
Hopf Algebras ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Group Algebras ◽  
Finite Abelian Groups ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Characteristic 2 ◽  
Nichols Algebras ◽  
Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

scholarly journals Sum-free subsets of finite abelian groups of type III

2016 ◽  
Vol 58 ◽  
pp. 181-202 ◽  
Author(s):  
R. Balasubramanian ◽  
Gyan Prakash ◽  
D.S. Ramana
Keyword(s):  
Abelian Groups ◽  
Finite Abelian Groups ◽  
Type Iii
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