Under any group action, a finite system of representatives of size r for a bounded family of sets can be replaced by an invariant system of representatives of size at most r times the maximum set size.
Khukhro-Makarenko type theorems for algebras
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abstract
We prove some anologues for algebras of recent group-theoretic results (due to Khukhro, Klyachko, Makarenko, Milentyeva, and Shumyatsky) on large characteristic subgroups satisfying a given property.
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2019 1verdicts
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Invariant systems of representatives, or The cost of symmetry
Under any group action, a finite system of representatives of size r for a bounded family of sets can be replaced by an invariant system of representatives of size at most r times the maximum set size.