Contents Introduction.................................................................................................................... 3 1. Preliminaries (topology & measure).................................................................... 3 2. Problems and the theorem.................................................................................... 7 3. Preliminaries (abstract groups, Cartesian products)....................................... 9 4. Preliminaries (automorphisms, duality theory).................................................. 13 5. Compact groups....................................................................................................... 15 6. Theorems on the groups $D_p$........................................................................... 18 7. A decomposition of compact groups.................................................................... 27 8. Groups in which all compact topologies are isomorphic................................ 33 9. The class M............................................................................................................... 40 10. Proof of the Main Theorem (groups of the class M)........................................ 42 11. Proof of tho Main Theorem (reduced groups).................................................. 47 12. Proof of the Main Theorem (conclusion)........................................................... 48 References.................................................................................................................... 57
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