• Corpus ID: 119588940

On an Inequality of Dimension-like Invariants for Finite Groups

@article{Fernando2015OnAI,
  title={On an Inequality of Dimension-like Invariants for Finite Groups},
  author={Ravi Fernando},
  journal={arXiv: Group Theory},
  year={2015}
}
  • Ravi Fernando
  • Published 2 February 2015
  • Mathematics
  • arXiv: Group Theory
In this paper, we introduce several notions of "dimension" of a finite group, involving sizes of generating sets and certain configurations of maximal subgroups. We focus on the inequality $m(G) \leq \mathrm{MaxDim}(G)$, giving a family of examples where the inequality is strict, and showing that equality holds if $G$ is supersolvable. 
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10 Citations
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Viewing P as a K-module via π, then, the P i form a chain of K-submodules of P . By complete reducibility, we can write P i+1 = P i ⊕ Q i+1 for some onedimensional submodules Q 1

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