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Papers by Bernhard Amberg
Advances in Group Theory and Applications, 2016
It is proved that a group which is the product of pairwise permutable abelian subgroups of finite... more It is proved that a group which is the product of pairwise permutable abelian subgroups of finite Prüfer rank is hyperabelian with finite Prüfer rank; in the periodic case the Sylow subgroups of such a product are described. Furthermore, if G=ABCG = ABCG=ABC is such a non-periodic product with locally cyclic subgroups A, B and C, then the Prüfer rank of GGG is at most 888. Moreover, GGG is soluble of derived length at most 444 and has Prüfer rank at most 6, if AcapBcapC=1A\cap B\cap C = 1AcapBcapC=1, and GGG has a torsion subgroup TTT such that the factor group G/TG/TG/T is locally cyclic and the Sylow ppp-subgroups of TTT are of Prüfer rank at most 222 for odd ppp and at most 666 for p=2p = 2p=2, otherwise.
Proceedings of the International Conference held at Pusan National University, Pusan, Korea, August 18-25, 1994, 1995
Canadian Journal of Mathematics, 1971
Pacific Journal of Mathematics, 1970
It still seems to be unknown whether there exist Noetherian groups (-groups with maximum conditio... more It still seems to be unknown whether there exist Noetherian groups (-groups with maximum condition on subgroups) that are not almost polycyclic, i.e., possess a soluble normal subgroup of finite index. However, the existence of even finitely generated infinite simple groups shows that in general a group whose subnormal subgroups satisfy the maximum condition need not be almost polycyclic. The following theorem gives a number of criteria for a group satisfying a weak form of the maximum condition to be almost polycyclic.
Rendiconti Del Seminario Matematico Della Università Di Padova, 1983
Illinois journal of mathematics
Rocky Mountain Journal of Mathematics, 1977
Introduction. If the group G = AB is the product of two of its subgroups A and B, then G is said ... more Introduction. If the group G = AB is the product of two of its subgroups A and B, then G is said to have a factorization with factors A and B, and G is factorized by its subgroups A and B. The main problem about factorized groups is the following question: What can be said about the structure of the factorized group G = AB if the structure of its subgroups A and B is known?
Mathematische Zeitschrift, 1971
Mathematische Annalen, 1968
Glasgow Mathematical Journal, 1985
If the group G = AB is the product of two abelian subgroups A and B, then G is metabelian by a we... more If the group G = AB is the product of two abelian subgroups A and B, then G is metabelian by a well-known result of Ito , so that the commutator subgroup G' of G is abelian. In the following we are concerned with the following condition:
Canadian Mathematical Bulletin, 1984
Archiv der Mathematik, 1968
Archiv der Mathematik, 1968
Archiv der Mathematik, 1978
Archiv der Mathematik, 1985
Advances in Group Theory and Applications, 2016
It is proved that a group which is the product of pairwise permutable abelian subgroups of finite... more It is proved that a group which is the product of pairwise permutable abelian subgroups of finite Prüfer rank is hyperabelian with finite Prüfer rank; in the periodic case the Sylow subgroups of such a product are described. Furthermore, if G=ABCG = ABCG=ABC is such a non-periodic product with locally cyclic subgroups A, B and C, then the Prüfer rank of GGG is at most 888. Moreover, GGG is soluble of derived length at most 444 and has Prüfer rank at most 6, if AcapBcapC=1A\cap B\cap C = 1AcapBcapC=1, and GGG has a torsion subgroup TTT such that the factor group G/TG/TG/T is locally cyclic and the Sylow ppp-subgroups of TTT are of Prüfer rank at most 222 for odd ppp and at most 666 for p=2p = 2p=2, otherwise.
Proceedings of the International Conference held at Pusan National University, Pusan, Korea, August 18-25, 1994, 1995
Canadian Journal of Mathematics, 1971
Pacific Journal of Mathematics, 1970
It still seems to be unknown whether there exist Noetherian groups (-groups with maximum conditio... more It still seems to be unknown whether there exist Noetherian groups (-groups with maximum condition on subgroups) that are not almost polycyclic, i.e., possess a soluble normal subgroup of finite index. However, the existence of even finitely generated infinite simple groups shows that in general a group whose subnormal subgroups satisfy the maximum condition need not be almost polycyclic. The following theorem gives a number of criteria for a group satisfying a weak form of the maximum condition to be almost polycyclic.
Rendiconti Del Seminario Matematico Della Università Di Padova, 1983
Illinois journal of mathematics
Rocky Mountain Journal of Mathematics, 1977
Introduction. If the group G = AB is the product of two of its subgroups A and B, then G is said ... more Introduction. If the group G = AB is the product of two of its subgroups A and B, then G is said to have a factorization with factors A and B, and G is factorized by its subgroups A and B. The main problem about factorized groups is the following question: What can be said about the structure of the factorized group G = AB if the structure of its subgroups A and B is known?
Mathematische Zeitschrift, 1971
Mathematische Annalen, 1968
Glasgow Mathematical Journal, 1985
If the group G = AB is the product of two abelian subgroups A and B, then G is metabelian by a we... more If the group G = AB is the product of two abelian subgroups A and B, then G is metabelian by a well-known result of Ito , so that the commutator subgroup G' of G is abelian. In the following we are concerned with the following condition:
Canadian Mathematical Bulletin, 1984
Archiv der Mathematik, 1968
Archiv der Mathematik, 1968
Archiv der Mathematik, 1978
Archiv der Mathematik, 1985