More generally, a finite group G is called a p-hyperelementary if it has the extension
where 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.
elementary, group, algebra, more, specifically, group, theory, elementary, group, direct, product, finite, cyclic, group, order, relatively, prime, group, finite, group, elementary, group, elementary, some, prime, number, elementary, group, nilpotent, brauer, . 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 C G P 1 displaystyle 1 longrightarrow C longrightarrow G longrightarrow P longrightarrow 1 where C displaystyle 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 See also editElementary abelian groupReferences editArthur Bartels Wolfgang Luck 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 nbsp This group theory related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Elementary group amp oldid 1170152471, wikipedia, wiki, book, books, library,
