What question did this study set out to answer?

To investigate the characteristics of relative M-groups in the context of finite groups and normal subgroups.

January 6, 2026Journal of Algebra and Its Applications0 citations

Relative M -groups and relative M p -groups

XCXiaoyou ChenHenan University of Technology JZJielin ZhangCenter for High Pressure Science & Technology Advanced Research YGYuting GaoShangqiu Institute of Technology

Key Points

To investigate the characteristics of relative M-groups in the context of finite groups and normal subgroups.
Defined relative M-groups with respect to normal subgroups
Analyzed relationships involving irreducible Brauer characters
Identified criteria for a subgroup to be a relative p-group
Presented results connecting subgroup structures and Brauer characters

Abstract

Let Formula: see text be a finite group and Formula: see text be a prime. Denote by Formula: see text the set of irreducible Formula: see textBrauer characters of Formula: see text. Let Formula: see text be a normal subgroup of Formula: see text. Formula: see text is said to be a relative Formula: see text-group with respect to Formula: see text if for every Brauer character Formula: see text, there exists a subgroup Formula: see text of Formula: see text containing Formula: see text and Formula: see text such that Formula: see text and Formula: see text. We obtain some results about relative Formula: see text-groups in this note.

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