Abstract
SupposeG is a finitep-group andk is the field ofp elements, and letU be the augmentation ideal of the group algebrakG. We investigate whichp-groups,G, have normal complements in their modp-envelope,G *.G * is defined byG *={1−u∶u∈U}.
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References
D. B. Coleman,On the modular group ring of a p-group, Proc. Amer. Math. Soc.15 (1964).
C. D. H. Cooper,Words which give rise to another group operation for a given group, Proc. Second Internat. Conf. Theory of Groups, Canberra, 1973 (Lecture Notes in Mathematics. Springer-Verlag, Berlin, Heidelberg, New York).
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Moran, L.E., Tench, R.N. Normal complements in modp-envelopes. Israel J. Math. 27, 331–338 (1977). https://doi.org/10.1007/BF02756491
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DOI: https://doi.org/10.1007/BF02756491