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In algebra, more specifically group theory, a p-elementary group is a direct product of a finite cyclic group of order relatively prime to p and a p-group. A finite group is an elementary group if it is p-elementary for some prime number p. An elementary group is nilpotent.

Brauer's theorem on induced characters states that a character on a finite group is a linear combination with integer coefficients of characters induced from elementary subgroups.

More generally, a finite group G is called a p-hyperelementary if it has the extension

$1\longrightarrow C\longrightarrow G\longrightarrow P\longrightarrow 1$

where $C$ is cyclic of order prime to p and P is a p-group. Not every hyperelementary group is elementary: for instance the non-abelian group of order 6 is 2-hyperelementary, but not 2-elementary. The term "hyperelementary" was introduced Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. by G. Segal.

References

• Arthur Bartels, Wolfgang Lück, Induction Theorems and Isomorphism Conjectures for K- and L-Theory
• G. Segal, The representation-ring of a compact Lie group
• J.P. Serre, "Linear representations of finite groups". Graduate Texts in Mathematics, vol. 42, Springer-Verlag, New York, Heidelberg, Berlin, 1977,

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