On metahamiltonian groups of infinite rank

groups of infinite rank with a normalizer condition on subgroups

groups of infinite rank in which every subgroup is either normal or self-normalizing are characterized in terms of their subgroups of infinite rank.

Crystal bases and combinatorics of infinite rank quantum groups

The tensor powers of the vector representation associated to an infinite rank quantum group decompose into irreducible components with multiplicities independant of the infinite root system considered. Although the irreducible modules obtained in this way are not of highest weight, they admit a crystal basis and a canonical basis. This permits in particular to obtain for each familly of classic...

groups whose proper subgroups of infinite rank have polycyclic-by-finite conjugacy classes

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. ...

On Infinite Groups

On the Loewy Rank of Infinite Algebras

The Loewy rank of a complete lattice L is deened as follows. Take the meet a 1 of all coatoms of L. Then let a 2 be the meet of all lower covers of a 1. Iterate this process to deene a for every ordinal by letting a +1 be the meet of all lower covers of a , and a the meet of all a (for <) if is a limit ordinal. The Loewy rank of L is the smallest ordinal for which a is the zero of L, and the sy...