In mathematical finite group theory, the Dempwolff group is a finite group of order 319979520 = 215·32·5·7·31, that is the unique nonsplit extension of by its natural module of order . The uniqueness of such a nonsplit extension was shown by Dempwolff (1972), and the existence by Thompson (1976), who showed using some computer calculations of Smith (1976) that the Dempwolff group is contained in the compact Lie group as the subgroup fixing a certain lattice in the Lie algebra of , and is also contained in the Thompson sporadic group (the full automorphism group of this lattice) as a maximal subgroup.
Huppert (1967, p.124) showed that any extension of by its natural module splits if . Note that this theorem does not necessarily apply to extensions of ; for example, there is a non-split extension , which is a maximal subgroup of the Lyons group. Dempwolff (1973) showed that it also splits if is not 3, 4, or 5, and in each of these three cases there is just one non-split extension. These three nonsplit extensions can be constructed as follows:
The nonsplit extension is a maximal subgroup of the Chevalley group .
The nonsplit extension is a maximal subgroup of the sporadic Conway group Co3.
The nonsplit extension is a maximal subgroup of the Thompson sporadic group Th.
In mathematical finite group theory, the Dempwolffgroup is a finite group of order 319979520 = 215·32·5·7·31, that is the unique nonsplit extension 2...
Chevalley group E8(3). The subgroup preserving the Lie bracket (over the integers) is a maximal subgroup of the Thompson group called the Dempwolffgroup (which...
languages were spoken on the islands, one reported by Thilenius and one by Dempwolff. "Kaniet". Ethnologue. Archived from the original on 2009-01-30. Retrieved...
other extant double-hulled voyaging canoes. The German linguist Otto Dempwolff (1934-1938) originally reconstructed the Proto-Austronesian word for "boat"...
on the history of the phonology was made by the German linguist Otto Dempwolff. It included a reconstruction of the Proto-Austronesian lexicon. The term...
Study". The Journal of the Polynesian Society. 41 (2 (162)): 131–143. Dempwolff, Otto (1934–1938). "Vergleichende Lautlehre des austronesischen Wortschatzes"...
to destroy the element of surprise. [Beevor, p. 112] Later Oberst Hugo Dempwolff After the war, served as commandant of the former Palace Hotel (called...
and little attention was paid by later scholars of the language group, Otto Dempwolff and Otto Dahl, in their reconstructions of the protolanguage. His...
although the meaning has shifted after Islamization. The linguist Otto Dempwolff has also theorized that *balian may have ultimately derived from Proto-Austronesian...
"Projective Planes of Order 27". ericmoorhouse.org. Retrieved 2020-11-08. Dempwolff 1994 "Projective Planes of Order 32". ericmoorhouse.org. Retrieved 2020-11-08...
second-hand accounts. The first Europeans to report meeting the Hadza are Otto Dempwolff and Erich Obst. The latter lived with them for eight weeks in 1911. German...
Möhring who was killed on 18 December 1944. Möhring was succeeded by Hugo Dempwolff. It then saw action in Luxembourg, and was destroyed fighting American...
to in detail, however, in unpublished correspondence dated 1927 from Dempwolff to Ray, so he obviously had copies passed on to others. John Lynch gathered...
care, he recovered before fleeing the hospital returning to Kabakon. Dempwolff, a German doctor at the hospital in Herbertshöhe, judged Engelhardt "a...
are considered to be unit phonemes rather than clusters. However, Otto Dempwolff, who greatly influenced the German missionary orthographies in New Guinea...
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