By Borovik A. V.
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Allow S be a finite non-trivial 2-group. it really is proven that there exists a nontrivial attribute subgroup W(S) in S satisfying:W(S) is basic in H for each finite Σ4-free teams H withSεSyl2(H) andC H(O2(H))≤O2(H).
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Not William I but Helmuth von Moltke led the armies in the campaigns of 1866 and 1870– 71. William II used to declare that in case of war he would personally command his armies, and that he needed a chief of staff only in peacetime. But when the first World War broke out this boasting was forgotten. Helmuth von Moltke’s nephew, a courtier without any military knowledge or ability, timid and irresolute, sick and nervous, an adept of the doubtful theosophy of Rudolph Steiner, led the German Army into the debacle at the Marne; then he collapsed.
The mere suggestion that a detachment could refuse to obey an order, or that men of the reserve when called to active duty might stay out, would have been considered an absurdity. The German nation had changed in a very remarkable way. We shall consider later the essence and cause of this great transformation. The main political problem of the 1850s and early 1860s, the problem of the reliability of the soldiers, had vanished. All German soldiers were now unconditionally loyal to the Supreme War Lord.
Herein too their successors proved inadequate. They were poor organizers and incompetent generals. The chief of the Great General Staff, who nominally was merely the King’s assistant, became virtually commander in chief. The change remained for a long time unnoticed. As late as the War of 1866 many high-ranking generals were still not aware of the fact that the orders they had to obey did not emanate from the King but from General von Moltke. Frederick II owed his military successes to a great extent to the fact that the Austrian, French, and Russian armies that he fought were not commanded by their sovereigns but by generals.
3-local characterization of Held groups by Borovik A. V.