One of the most important problems of fuzzy group theory is to classify the fuzzy subgroups of a finite group. This topic has enjoyed a rapid development in the last few years. Several papers have treated the particular case of finite abelian groups. Thus, in [13] the number of distinct fuzzy subgroups of a finite cyclic group of square-free order is determined, while [14–16] and [28] deal with...

Integral sets of finite groups are discussed and related to the integral Cayley graphs. The Boolean algebra of integral sets are determined for dihedral group and finite abelian groups. We characterize the finite abelian groups as those finite groups where the Boolean algebra generated by integral sets equals the Boolean algebra generated by its subgroups.

a group g is said to be a (pf)c-group or to have polycyclic-by-finite conjugacy classes, if g/c_{g}(x^{g}) is a polycyclic-by-finite group for all xin g. this is a generalization of the familiar property of being an fc-group. de falco et al. (respectively, de giovanni and trombetti) studied groups whose proper subgroups of infinite rank have finite (respectively, polycyclic) conjugacy classes. ...

We give a simple proof of the finite presentation of Sela's limit groups by using free actions on R n-trees. We first prove that Sela's limit groups do have a free action on an R n-tree. We then prove that a finitely generated group having a free action on an R n-tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic ...

We give a simple proof of the finite presentation of Sela's limit groups by using free actions on R n-trees. We first prove that Sela's limit groups do have a free action on an R n-tree. We then prove that a finitely generated group having a free action on an R n-tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic ...

We give a simple proof of the finite presentation of Sela’s limit groups by using free actions on Rn–trees. We first prove that Sela’s limit groups do have a free action on an Rn–tree. We then prove that a finitely generated group having a free action on an Rn–tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic gro...

The role of finite centralizers involutions in pseudo-finite groups is analyzed. It shown that a group admitting definable involutory automorphism fixing only finitely many elements finite-by-abelian-by-finite. As consequence, we give model-theoretic proof result for periodic due to Hartley and Meixner. Furthermore, it any has an infinite abelian subgroup.

Let be a finite abelian p-group. We the complete set of cross numbers of minimal sequences associated with G. We also result of Krause minimal zero sequences with cross numbers less than or Let G be an additively written finite abelian group and S = use exponentiation to represent in the sequence. We say that S is a zero sequence if 9i = o.