Group Algebras: An Upper Bound for the Davenport Constant

2013 ◽  
pp. 265-270
Author(s):  
David J. Grynkiewicz
Keyword(s):  
Upper Bound ◽  
Group Algebras ◽  
Davenport Constant

scholarly journals An upper bound for the Davenport constant of finite groups

2014 ◽  
Vol 218 (10) ◽  
pp. 1838-1844 ◽  
Author(s):  
Weidong Gao ◽  
Yuanlin Li ◽  
Jiangtao Peng
Keyword(s):  
Finite Groups ◽  
Upper Bound ◽  
Davenport Constant

ON DAVENPORT'S CONSTANT

2008 ◽  
Vol 04 (01) ◽  
pp. 107-115 ◽  
Author(s):  
P. RATH ◽  
K. SRILAKSHMI ◽  
R. THANGADURAI
Keyword(s):  
Abelian Group ◽  
Upper Bound ◽  
Davenport Constant ◽  
The Given

In this paper, using the idea of Alford, Granville and Pomerance in [1] (or van Emde Boas and Kruyswijk [6]), we obtain an upper bound for the Davenport Constant of an Abelian group G in terms of the number of repetitions of the group elements in any given sequence. In particular, our result implies, [Formula: see text] where n is the exponent of G and k ≥ 0 denotes the number of distinct elements of G that are repeated at least twice in the given sequence.

A note on Lie nilpotent group algebras

2019 ◽  
Vol 18 (09) ◽  
pp. 1950163
Author(s):  
Meena Sahai ◽  
Bhagwat Sharan
Keyword(s):  
Abelian Group ◽  
Nilpotent Group ◽  
Group Algebra ◽  
Upper Bound ◽  
Finite Abelian Group ◽  
Index Formula ◽  
Group Algebras ◽  
Arbitrary Group ◽  
Nilpotency Index

Let [Formula: see text] be an arbitrary group and let [Formula: see text] be a field of characteristic [Formula: see text]. In this paper, we give some improvements of the upper bound of the lower Lie nilpotency index [Formula: see text] of the group algebra [Formula: see text]. We also give improved bounds for [Formula: see text], where [Formula: see text] is the number of independent generators of the finite abelian group [Formula: see text]. Furthermore, we give a description of the Lie nilpotent group algebra [Formula: see text] with [Formula: see text] or [Formula: see text]. We also show that for [Formula: see text] and [Formula: see text], [Formula: see text] if and only if [Formula: see text], where [Formula: see text] is the upper Lie nilpotency index of [Formula: see text].

scholarly journals On the Davenport constant and group algebras

2010 ◽  
Vol 121 (2) ◽  
pp. 179-193 ◽  
Author(s):  
Daniel Smertnig
Keyword(s):  
Group Algebras ◽  
Davenport Constant
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