Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group identities on symmetric units under oriented involutions in group
  algebras   Let $\mathbb{F}G$ denote the group algebra of a locally finite group $G$ over
the infinite field $\mathbb{F}$ with $char(\mathbb{F})\neq 2$, and let
$\circledast:\mathbb{F}G\rightarrow \mathbb{F}G$ denote the involution defined
by $\alpha=\Sigma\alpha_{g}g \mapsto
\alpha^\circledast=\Sigma\alpha_{g}\sigma(g)g^{\ast}$, where
$\sigma:G\rightarrow \{\pm1\}$ is a group homomorphism (called an orientation)
and $\ast$ is an involution of the group $G$. In this paper we prove, under
some assumptions, that if the $\circledast$-symmetric units of $\mathbb{F}G$
satisfies a group identity then $\mathbb{F}G$ satisfies a polynomial identity,
i.e., we give an affirmative answer to a Conjecture of B. Hartley in this
setting. Moreover, in the case when the prime radical $\eta(\mathbb{F}G)$ of
$\mathbb{F}G$ is nilpotent we characterize the groups for which the symmetric
units $\mathcal{U}^+(\mathbb{F}G)$ do satisfy a group identity.

6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con