Singularity of mixed identities in infinite simple locally finite groups

Establish that every mixed identity of an infinite simple locally finite group is singular.

Background

The paper proves that every mixed identity is singular for all infinite simple locally finite groups except potentially groups of Lie types B_n, C_n, F_4, and G_2 over infinite locally finite fields. The conjecture asks whether the exceptional families also admit only singular mixed identities, thereby completing the classification of mixed identities in infinite simple locally finite groups.

References

In view of Theorems~\ref{thm:main} and \ref{thm:main_finintro}, the following two related conjectures seem natural. The following hold: Every mixed identity of an infinite simple locally finite group is singular.

— Mixed identities for simple locally finite groups  (2608.14537 - Bradford et al., 14 Aug 2026) in Introduction, Conjecture 1(i), labeled \ref{conj:main_lfsg}

We show that Conjecture~\ref{conj:main_lfsg}(ii) implies Conjecture \ref{conj:main_lfsg}(i); the converse implication is unclear to us.

— Mixed identities for simple locally finite groups  (2608.14537 - Bradford et al., 14 Aug 2026) in Introduction, paragraph immediately preceding Theorem \ref{thm:strictsimpleintro}