What does this research mean for the field?

The symmetric units of the group ring FG satisfy a bounded Engel identity under specific conditions related to the group's structure and the characteristic of the field. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Investigate conditions for symmetric units in group rings to satisfy bounded Engel identities.

March 12, 2026Open Access

Bounded Engel symmetric units in group rings

Key Points

Investigate conditions for symmetric units in group rings to satisfy bounded Engel identities.
Examined properties of group G under torsion and p-elements conditions.
Considered group rings FG with respect to the classical involution.
Analyzed the implications of the field's characteristic on symmetric units.
Identified specific criteria for G being torsion or having finitely many p-elements.
Established that symmetric units satisfy bounded Engel identities under the given conditions.

Abstract

Let G be a group and F an infinite field of characteristic p ≠ 2 . If either G is torsion, or p > 2 and G has only finitely many p -elements, we determine the conditions under which the symmetric units of the group ring FG , with respect to the classical involution, satisfy a bounded Engel identity.

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Cite This Study

Lee et al. (Sun,) studied this question.

synapsesocial.com/papers/69b2581996eeacc4fcec76df https://doi.org/https://doi.org/10.1016/j.jalgebra.2026.03.003

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