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<p>This article focuses on the study of <Emphasis FontCategory="SansSerif">cut</Emphasis> groups, i.e., the groups which have only trivial central units in their integral group ring. We provide state of the art for <Emphasis FontCategory="SansSerif">cut</Emphasis> groups. The results are compiled in a systematic manner and have also been analogously studied for some generalized classes, such as quadratic rational groups and semi-rational groups etc. For these bigger classes, some results have been extended, while others have been posed as questions. The progress and the problems signify the development and the potential that holds in the topic of <Emphasis FontCategory="SansSerif">cut</Emphasis> groups and its generalizations.</p>

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Cut groups: the progress and the problems

  • 期刊论文

  • 发表日期：

    2026年7月21日

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  • Seema Chahal,
  • Sugandha Maheshwary

摘要

This article focuses on the study of cut groups, i.e., the groups which have only trivial central units in their integral group ring. We provide state of the art for cut groups. The results are compiled in a systematic manner and have also been analogously studied for some generalized classes, such as quadratic rational groups and semi-rational groups etc. For these bigger classes, some results have been extended, while others have been posed as questions. The progress and the problems signify the development and the potential that holds in the topic of cut groups and its generalizations.