Splitting of abelian-by-hyperfinite groups

Ｓｐｌｉｔｔｉｎｇｏｆａｂｅｌｉａｎ－ｂｙ－ｈｙｐｅｒｆｉｎｉｔｅｇｒｏｕｐｓＤｕａｎＺｅｙｏｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓＳｏｕｔｈｗｅｓｔＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｃｈｏｎｇｑｉｎｇ６３０７１５）Ｓｐｌｉｔ...

Let be a locally defined formation consisting of periodic locally soluble groups and let Ebe an extension of an abelian group A by a hyperfinite locally soluble group G . If and A is ahyperfinite artinian ZE-module with, then it was known that E splits conjugately over A . Thesame result for A being noetherian is proved.