Finite p0-Semiregular Groups
نویسنده
چکیده
About 60 years ago H. Zassenhaus 17] classiied nite near-elds. In doing so he also gave a full description of those nite groups which have a representation D (over C) such that D(g) has no eigenvalue 1 for any nontrivial element g 2 G. In our terminology such a group is called semiregular. One of the results in 17] characterizes SL 2 (5) as the only perfect semiregular group. Clearly, if the underlying eld F has characteristic p dividing the group order, then p-elements of G always act with eigenvalue 1 on any F G-module. So in this situation the notion of 'semiregularity' naturally modiies to a local version which in this paper is called 'p 0-semiregularity' (cf. 1.1). Of course this localized semiregularity can also be studied in the complex case. In particular a nite group is semiregular if and only if it is p 0-semiregular for all primes p.
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