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M-group

In mathematics, especially in the field of group theory, the term M-group may refer to a few distinct concepts:

• In the area studying the character theory of finite groups, an M-group or monomial group is a group whose complex irreducible characters are all monomial, that is, induced from linear characters.
• In the area studying the lattice of subgroups of a group, an M-group or modular group or Iwasawa group is a group in which every subgroup is modular
• In the textbook (Scott 1964, Ch 7.1) and some papers, an M-group refers to what is now called a polycyclic-by-finite group, which by Hirsch's theorem can also be expressed as a group which has a finite length normal series with each factor a finite group or an infinite cyclic group.