The crucial 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, particularly these of BAER and ORE, a wide physique of literature has grown up round this idea, and it's our goal to provide an image of the current kingdom of this thought. to acquire a scientific remedy of the topic numerous unpublished result of the writer needed to be incorporated. however, it really is normal that shall we no longer reproduce each aspect and needed to deal with a few components a few wh at sketchily. now we have attempted to make this document as self-contained as attainable. for this reason we've got given a few proofs in huge aspect, notwithstanding after all it really is within the nature of such areport that many proofs must be passed over or can basically receive in define. equally references to the recommendations and theorems used are virtually completely references to plain works like BIRKHOFF [lJ and ZASSENHAUS [lJ. the writer want to show his honest gratitude to Professors REINHOLD BAER and DONALD G. HIGMAN for his or her kindness in giving hirn many worthy feedback. His thank you also are as a result of Dr. NOBORU ITo who, in the course of stimulating conversations, contributed many beneficial principles. Urbana, might, 1956. M. Suzuki. Contents.
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