Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: C-loops: An introduction   C-loops are loops satisfying $x(y(yz))=((xy)y)z$. They often behave
analogously to Moufang loops and they are closely related to Steiner triple
systems and combinatorics. We initiate the study of C-loops by proving: (i)
Steiner loops are C-loops, (ii) C-loops are alternative, inverse property loops
with squares in the nucleus, (iii) the nucleus of a C-loop is a normal
subgroup, (iv) C-loops modulo their nucleus are Steiner loops, (v) C-loops are
power associative, power alternative but not necessarily diassociative, (vi)
torsion commutative C-loops are products of torsion abelian groups and torsion
commutative 2-C-loops; and several other results. We also give examples of the
smallest nonassociative C-loops, and explore the analogy between commutative
C-loops and commutative Moufang loops.

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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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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: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: hep-lat