Abstract
Let \(G\) be a locally compact \(\sigma \)-compact Abelian group and let \(G^{LUC}\) denote the largest semigroup compactification of \(G\). We show that for every finite group \(Q\) in \(G^*=G^{LUC}{\setminus } G\) with identity \(u\), there is a finite group \(F\) in \(G\) such that \(Q=Fu\). In particular, if \(G\) contains no nontrivial finite group, neither does \(G^{LUC}\).
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Acknowledgments
This study was supported by NRF Grant IFR2011033100072.
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Communicated by Jimmie D. Lawson.
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Zelenyuk, Y. Finite groups in \(G^{LUC}\) . Semigroup Forum 91, 316–320 (2015). https://doi.org/10.1007/s00233-014-9652-6
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DOI: https://doi.org/10.1007/s00233-014-9652-6