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A group topology on the free abelian group of cardinality c that makes its square countably compact
(POLISH ACAD SCIENCES INST MATHEMATICS, 2011)
Under p = c, we prove that it is possible to endow the free abelian group of cardinality c with a group topology that makes its square countably compact. This answers a question posed by Madariaga-Garcia and Tomita and by ...
ALTERNATING UNITS AS FREE FACTORS IN THE GROUP OF UNITS OF INTEGRAL GROUP RINGS
(CAMBRIDGE UNIV PRESS, 2011)
Let G be a group of odd order that contains a non-central element x whose order is either a prime p >= 5 or 3(l), with l >= 2. Then, in U(ZG), the group of units of ZG, we can find an alternating unit u based on x, and ...
The domino problem on groups of polynomial growth
(European Mathematical Society, 2018)
We conjecture that a finitely generated group has a decidable domino problem if and only if it is virtually free. We show this is true for all virtually nilpotent finitely generated groups (or, equivalently, groups of ...
THE M-ORDERED REAL FREE PRO-2-GROUP - COHOMOLOGICAL CHARACTERIZATIONS
(Marcel Dekker IncNew York, 1993)
BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS
(WORLD SCIENTIFIC PUBL CO PTE LTD, 2011)
Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass ...
SUBDIRECT PRODUCTS OF FREE PRO-p AND DEMUSHKIN GROUPS
(World Scientific Publ Co Pte LtdSingaporeSingapura, 2013)
Free actions of abelian p-groups on the n-Torus
(2005-01-01)
In this work we make some contributions to the theory of actions of abelian p-groups on the n-Torus Tn. Set H ≅ ℤpk1 h1 × ℤpk2h2 × ⋯ × ℤpkrhr, r ≥ 1, k1 ≥ k2 ≥ ⋯ ≥ kr ≥ 1, p prime. Suppose that the group H acts freely on ...
Fully residually free pro-p groups
(Academic Press Inc Elsevier ScienceSan DiegoEUA, 2010)
INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS
(WORLD SCIENTIFIC PUBL CO PTE LTD, 2011)
Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let * be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form ...
Hyperbolic unit groups and quaternion algebras
(INDIAN ACAD SCIENCES, 2009)
We classify the quadratic extensions K = Q[root d] and the finite groups G for which the group ring o(K)[G] of G over the ring o(K) of integers of K has the property that the group U(1)(o(K)[G]) of units of augmentation 1 ...