On medium-size subgroups and bases of finite groups

@article{Bertram1991OnMS,
  title={On medium-size subgroups and bases of finite groups},
  author={Edward A. Bertram and Marcel Herzog},
  journal={J. Comb. Theory, Ser. A},
  year={1991},
  volume={57},
  pages={1-14}
}
In this paper G denotes a finite group. A subset A of G is called a basis of G if A2 = G, where A2 = (ab 1 a, b E A }. The minimal cardinality of a basis of G will be denoted by v(G). The problem of estimating r(G) for cyclic groups was first proposed by I. Schur and various bounds were obtained by Rohrbach [Rl], Moser [M], Stohr [S], Klotz [K], and others. In [R2], Rohrbach dealt with bases for arbitrary groups. This paper incorporates the results of [R2]. The aim of this paper is to find… CONTINUE READING

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