The important subject of this monograph is the relation among the constitution of a bunch and the constitution of its lattice of subgroups. because the first papers in this subject have seemed, significantly these of BAER and ORE, a wide physique of literature has grown up round this thought, and it really is our goal to provide an image of the current country of this concept. to acquire a scientific remedy of the topic a variety of unpublished result of the writer needed to be integrated. nevertheless, it really is common that shall we no longer reproduce each element and needed to deal with a few elements a few wh at sketchily. we've attempted to make this file as self-contained as attainable. consequently now we have given a few proofs in huge element, although in fact it truly is within the nature of such areport that many proofs must be passed over or can basically take delivery of in define. equally references to the options and theorems used are virtually completely references to straightforward works like BIRKHOFF [lJ and ZASSENHAUS [lJ. the writer want to convey his honest gratitude to Professors REINHOLD BAER and DONALD G. HIGMAN for his or her kindness in giving hirn many necessary feedback. His thank you also are as a result of Dr. NOBORU ITo who, in the course of stimulating conversations, contributed many beneficial rules. Urbana, may perhaps, 1956. M. Suzuki. Contents.
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