We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbit...We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbitrary field of characteristic p. The proof uses Auslander-Reiten theory.展开更多
The Shanghai Cooperation Organization (SOC), made up of six member countries, is reinventing itself and banding together to deal with the region's security and economic development. Operating under the "Shang...The Shanghai Cooperation Organization (SOC), made up of six member countries, is reinventing itself and banding together to deal with the region's security and economic development. Operating under the "Shanghai Spirit"-the essence of state-to-state relations where trust and equality are key to members looking out for each other-questions need to be asked and answered at the organization's fifth anniversary. Despite the best intentions, a clear road map is needed to clarify the SCO's future.展开更多
基金the Japan Society for Promotion of Science （JSPS）, Grant-in-Aid for Scientific Research （C）15K04776, 2015-2018, and by the CIB in EPFL. The second author was supported by the German Science Foundation （DFG） Scientific Priority Programme SPP-1489 ＂Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory＂.
文摘We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbitrary field of characteristic p. The proof uses Auslander-Reiten theory.
文摘The Shanghai Cooperation Organization (SOC), made up of six member countries, is reinventing itself and banding together to deal with the region's security and economic development. Operating under the "Shanghai Spirit"-the essence of state-to-state relations where trust and equality are key to members looking out for each other-questions need to be asked and answered at the organization's fifth anniversary. Despite the best intentions, a clear road map is needed to clarify the SCO's future.
