Geodesic
Bases in dihedral and Boolean groups
Journal of integer sequences, Tome 20 (2017) no. 8
A subset $B$ of a group $G$ is called a $basis$ of $G$ if $G = B^{2}$. The smallest cardinality of a basis of $G$ is called the basis size of $G$. We prove upper bounds for basis sizes of dihedral and Boolean groups. We find a lower bound for the basis size of a Boolean group. We also calculate basis sizes for dihedral and Boolean groups of small orders.
Classification : 05B10, 05E15, 20D60
Keywords: dihedral group, Boolean group, basis, basis size, basis characteristic 
@article{JIS_2017__20_8_a0,
     author = {Gavrylkiv,  Volodymyr},
     title = {Bases in dihedral and {Boolean} groups},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {8},
     zbl = {1368.05016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_8_a0/}
}
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Gavrylkiv,  Volodymyr. Bases in dihedral and Boolean groups. Journal of integer sequences, Tome 20 (2017) no. 8. http://geodesic.mathdoc.fr/item/JIS_2017__20_8_a0/