Bounds for the rank of the finite part of operator K-theory

We derive a lower and an upper bound for the rank of the finite part of operator K-theory groups of maximal and reduced C*-algebras of finitely generated groups. The lower bound is based on the amount of polynomially growing conjugacy classes of finite order elements in the group. The upper bound is based on the amount of torsion elements in the group. We use the lower bound to give lower bounds for the structure group S(M) and the group of positive scalar curvature metrics P (M) for an oriented manifold M.


On a Fitting length conjecture without the coprimeness condition
Ercan, Gülin (Springer Science and Business Media LLC, 2012-08-01)
Let A be a finite nilpotent group acting fixed point freely by automorphisms on the finite solvable group G. It is conjectured that the Fitting length of G is bounded by the number of primes dividing the order of A, counted with multiplicities. The main result of this paper shows that the conjecture is true in the case where A is cyclic of order p (n) q, for prime numbers p and q coprime to 6 and G has abelian Sylow 2-subgroups.
On local finiteness of periodic residually finite groups
Kuzucouoglu, M; Shumyatsky, P (2002-10-01)
Let G be a periodic residually finite group containing a nilpotent subgroup A such that C-G (A) is finite. We show that if [A, A(g)] is finite for any g is an element of G, then G is locally finite.
Direct limits of monomial groups
Kuzucuoğlu, Mahmut (null; 2017-01-23)
We give the construction of homogenous monomial groups as a direct limit of monomial groups. Then we find the structure of the centralizers of elements and conjugacy of two elements in homogenous monomial groups. Moreover isomorphisms of two homogenous monomial groups will be discussed.
On the influence of fixed point free nilpotent automorphism groups
Ercan, Gülin (2017-12-01)
A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that for all nonidentity elements . Let FH be a Frobenius-like group with complement H of prime order such that is of prime order. Suppose that FH acts on a finite group G by automorphisms where in such a way that In the present paper we prove that the Fitting series of coincides with the intersections of with the Fitting series of G, and the nilpotent length of G exceeds the...
The classical involution theorem for groups of finite Morley rank
Berkman, A (Elsevier BV, 2001-09-15)
This paper gives a partial answer to the Cherlin-Zil'ber Conjecture, which states that every infinite simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field. The classification of the generic case of tame groups of odd type follows from the main result of this work, which is an analogue of Aschbacher's Classical Involution Theorem for finite simple groups. (C) 2001 Academic Press.
Citation Formats
S. K. Samurkaş, “Bounds for the rank of the finite part of operator K-theory,” JOURNAL OF NONCOMMUTATIVE GEOMETRY, vol. 14, no. 2, pp. 413–439, 2020, Accessed: 00, 2021. [Online]. Available: