J Austral Math Soc Ser A 44 pp225--232, 1988.

Chief Series and Right Regular Representations of Finite p-Groups

Felix Leinen

Abstract

We study the embeddings of a finite p-group U into Sylow p-subgroups of Sym(U) induced by the right regular representation r: U ® Sym(U). It turns out that there is a one-to-one correspondence between the chief series in U and the Sylow p-subgroups of Sym(U) containing U_r. Here, the Sylow p-subgroup P_S of Sym(U) corresponding to the chief series S in U is characterized by the property that the intersections of U_r with the terms of any chief series in P_S form S_r. Moreover, we see that r: U ® P_S are precisely the kinds of embeddings used in a previous paper to construct the non-trivial countable algebraically closed locally finite p-groups as direct limits of finite p-groups.

1980 AMS Subject Classification: 20D15, 20B35

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Authors

Felix Leinen

Fachbereich 17-Mathematik, Johannes-Gutenberg-Universität, Saarstr. 21, 6500 Mainz, West Germany.