Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on finite groups with an automorphism inverting or squaring a
  non-negligible fraction of elements   We show that for a finite group $G$, the commuting probability of $G$ can be
explicitly bounded from below in a nontrivial way by a function in the maximum
fraction of elements inverted resp. squared by an automorphism of $G$. Using
these bounds together with a result of Guralnick and Robinson gives upper
bounds on the index of the Fitting subgroup of $G$ under each of the two
conditions that $G$ have an automorphism inverting resp. squaring at least
$\rho|G|$ many elements in $G$, for $\rho\in\left(0,1\right]$ fixed. This is an
improvement on previous results of the author.

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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: eess