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A note on generic subsets of definable groups

Mário J. Edmundo, G. Terzo (2011)

Fundamenta Mathematicae

We generalize the theory of generic subsets of definably compact definable groups to arbitrary o-minimal structures. This theory is a crucial part of the solution to Pillay's conjecture connecting definably compact definable groups with Lie groups.

A note on group algebras of p -primary abelian groups

William Ullery (1995)

Commentationes Mathematicae Universitatis Carolinae

Suppose p is a prime number and R is a commutative ring with unity of characteristic 0 in which p is not a unit. Assume that G and H are p -primary abelian groups such that the respective group algebras R G and R H are R -isomorphic. Under certain restrictions on the ideal structure of R , it is shown that G and H are isomorphic.

A note on groups with few isomorphism classes of subgroups

Francesco de Giovanni, Alessio Russo (2016)

Colloquium Mathematicae

The structure of infinite groups in which any two (proper) subgroups of the same cardinality are isomorphic is described within the universe of locally graded groups. The corresponding problem for finite groups was considered by R. Armstrong (1958).

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