Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Semi-Rational Groups   A finite group is called semi-rational if the distribution induced on it by
any word map is a virtual character. Amit and Vishne give a sufficient
condition for a group to be semi-rational, and ask whether it is also
necessary. We answer this in the negative, by exhibiting two new criteria for
semi-rationality, each giving rise to an infinite family of semi-rational
groups which do not satisfy the Amit-Vishne condition. On the other hand, we
use recent work of Lubotzky to show that for finite simple groups the
Amit-Vishne condition is indeed necessary, and we use this to construct the
first known example of an infinite family of non-semi-rational groups.

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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom