Let $ D $ be a weakly locally finite division ring and $ n $ a positive integer. The problem
under study concerns the existence of noncyclic free subgroups in noncentral almost …

Let D be a division algebra of finite dimension over its center F. Given a noncommutative
maximal subgroup M of D*≔ GL1 (D), it is proved that either M contains a noncyclic free …

The following conjecture is investigated: a noncentral subnormal subgroup of the
multiplicative group of a division ring contains a noncyclic free subgroup. Special cases are …

LetAbe a quaternion algebra over a commutative unital ring. We find sufficient conditions for
pairs of units ofAto generate a free group. Using the well-known isomorphism betweenSO …

Finitely Generated Subnormal Subgroups of GL_{n} (D) Are Central Page 1 Journal of Algebra
225, 517–521 (2000) doi:10.1006/jabr.1999.8096, available online at http://www.idealibrary.com …

Let D be a division ring with center Z and multiplicative group D∖{0}= D•, and let N be a
normal subgroup of D•. We investigate various conditions under which N must contain a free …

Let D be a division ring with center k, and let D† be its multiplicative group. We investigate
the existence of free groups in D†, and free algebras and free group algebras in D. We also …

A division ring D is said to be weakly locally finite if for every finite subset S ⊂ DS⊂ D, the
division subring of D generated by S is centrally finite. It is known that the class of weakly …

Let F be an algebraically closed field and let R be a locally finite algebra over F. This paper
aims to show that any element of R is a product of at most three unipotent elements from R if …

Let D be a division ring with an involution and characteristic different from 2. Then, up to a
few exceptions, D contains a pair of symmetric elements freely generating a free subgroup of …