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The Artin exponent of finite groups. (English) Zbl 0931.20010
The following main result is proved: Let $$G$$ be a finite $$p$$-group and $$e(G)$$ the Artin exponent induced from the elementary Abelian subgroup of $$G$$. One has the following: (1) If $$G$$ is Abelian then $$e(G)=|G:U|$$, where $$U$$ is the maximal elementary Abelian subgroup of $$G$$. (2) If $$G$$ is a quaternion or dihedral group then $$e(G)=2$$, and $$e(G)=4$$ if $$G$$ is the semidihedral group. (3) In all other cases $$e(G)=|G|/p$$.
##### MSC:
 20C15 Ordinary representations and characters 20D15 Finite nilpotent groups, $$p$$-groups 19A22 Frobenius induction, Burnside and representation rings
##### Keywords:
Artin exponents; Abelian groups; finite $$p$$-groups
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##### References:
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