Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal Covers of Finite Groups   Motivated by quotient algorithms, such as the well-known $p$-quotient or
solvable quotient algorithms, we describe how to compute extensions $\tilde H$
of a finite group $H$ by a direct sum of isomorphic simple $\mathbb{Z}_p
H$-modules such that $H$ and $\tilde H$ have the same number of generators.
Similar to other quotient algorithms, our description will be via a suitable
covering group of $H$. Defining this covering group requires a study of the
representation module, as introduced by Gasch\"utz in 1954. Our investigation
involves so-called Fox derivatives (coming from free differential calculus)
and, as a by-product, we prove that these can be naturally described via a
wreath product construction. An important application of our results is that
they can be used to compute, for a given epimorphism $G\to H$ and simple
$\mathbb{Z}_p H$-module $V$, the largest quotient of $G$ that maps onto $H$
with kernel isomorphic to a direct sum of copies of $V$. For this we also
provide a description of how to compute second cohomology groups for the (not
necessarily solvable) group $H$, assuming a confluent rewriting system for $H$.
To represent the corresponding group extensions on the computer, we introduce a
new hybrid format that combines this rewriting system with the polycyclic
presentation of the module.

28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph