... QED n = |G| . ... B] Ken Brown, Mathematics 4340, When are all groups of order n cyclic? ... http://olympiads.mccme.ru/lktg/2011/6/index.htm WHEN ANY GROUP OF N ELEMENTS IS CYCLIC? ... Thus |G| is divisible by m. QED A maximal subgroup of a group is a maximal by inclusion subgroup not coinciding with G and containing more than one element. ... 1) Any maximal subgroup F contains the center Z = Z (G) := {a G : g a = ag for any g G}, i.e., the set of elements commuting with each element of the group. ...

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... There are corresponding results showing that the Poincare duals of certain totally ge odesic cycles, which we will call "special cycles", span a definite part (a refined Hodge component) of the cohomology of the locally symmetric spaces of standard arithmetic type associated to the orthogonal groups O(p, q). ... Math. ... KLM3] (with B. Leeb and M. Kapovich) The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra, Memoirs of the AMS, Vol. ...

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