Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizing finite $p$-groups by their Schur multipliers   It has been proved in \cite{ge} for every $p$-group of order $p^n$,
$|\mathcal{M}(G)|=p^{\f{1}{2}n(n-1)-t(G)}$, where $t(G)\geq 0$. In \cite{be,
el, zh}, the structure of $G$ has been characterized for $t(G)=0,1,2,3$ by
several authors. Also in \cite{sa}, the structure of $G$ characterized when
$t(G)=4$ and $Z(G)$ is elementary abelian. This paper is devoted to classify
the structure of $G$ when $t(G)=4$ without any condition.

4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th