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Identifies five unique non-perfect finite groups that are X-decomposable, suggesting limitations in their structure.
Let [Formula: see text] be a finite group and [Formula: see text]. Then [Formula: see text] is called [Formula: see text]-decomposable in [Formula: see text] if it is a union of [Formula: see text] distinct [Formula: see text]-conjugacy classes, and denote [Formula: see text] by [Formula: see text]. A group [Formula: see text] is called [Formula: see text]-decomposable with [Formula: see text]. This paper proves that there are only five (isomorphism classes) [Formula: see text]-decomposable finite groups which are non-perfect.
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Guan et al. (2026) studied this question.
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