4 citations · 17 across the 24 of their papers we have counts for
34 papers
Homomorphisms from topological groups to inverse limits
Gregory R. Conner, Samuel M. Corson, Curtis Kent
We prove a general theorem giving constraints on maps from certain topological groups to inverse limits of bounded torsion groups. From this we obtain some automatic continuity and…
The double cone group is isomorphic to the archipelago group
Samuel M. Corson
We prove the conjecture of James W. Cannon and Gregory R. Conner that the fundamental group of the Griffiths double cone space is isomorphic to that of the harmonic archipelago. Fr…
Infinite simple groups with no proper abnormal subgroups
Samuel M. Corson
Utilizing an embedding theorem of Obraztsov we construct groups as described in the title. This provides an affirmative answer to a problem of D. O. Revin. The constructed groups a…
Bounded displacement permutations on tree-like spaces
Samuel M. Corson
It is shown that if a metric space exhibits certain finiteness and tree-like properties, then its group of bounded displacement does not include a subgroup isomorphic to the dyadic…
A permutation group acting transitively on certain collections of models
Samuel M. Corson, Saharon Shelah
It is shown, from -centered Martin's Axiom, that there exists a proper dense subgroup of the symmetric group on a countably infinite set whose natural action on sufficiently fle…
On homomorphic images of ultraproducts
Samuel M. Corson
In this short note we answer some questions of Bergman regarding homomorphic images of (ultra)products of groups.
Artinian groups of large cardinality
Samuel M. Corson, Saharon Shelah
A group is Artinian if there is no infinite strictly descending chain of subgroups. Ol'shanskii has asked whether there are Artinian groups of arbitrarily large cardinality. We sho…
Profinite rigidity of affine Coxeter groups
Samuel M. Corson, Sam Hughes, Philip Möller +1
We prove that affine Coxeter groups are profinitely rigid.
Higman-Thompson groups and profinite properties of right-angled Coxeter groups
Samuel M. Corson, Sam Hughes, Philip Möller +1
We prove that every right-angled Coxeter group (RACG) is profinitely rigid amongst all Coxeter groups. On the other hand we exhibit RACGs which have infinite profinite genus amongs…
Steep uncountable groups
Samuel M. Corson, Alexander Olshanskii, Olga Varghese
We produce a simple group of cardinality which is Artinian (every strictly descending chain of subgroups is finite), satisfies a Burnside law and such that for each…
On projections of the tails of a power
Samuel M. Corson, Saharon Shelah
Let be an inaccessible cardinal, be a universal algebra, and be the equivalence relation on of eventual equality. From mild assumptions o…
The nonabelian product modulo sum
Samuel M. Corson
It is shown that if is a sequence of groups without involutions, with , then the topologist's product modulo the finite words is (u…
Jónsson groups of various cardinalities
Samuel M. Corson
A group is Jónsson if whenever is a proper subgroup of . Using an embedding theorem of Obraztsov it is shown that there exists a Jónsson group of infinit…
The Griffiths double cone group is isomorphic to the triple
Samuel M. Corson
It is shown that the fundamental group of the Griffiths double cone space is isomorphic to that of the triple cone. More generally if is a cardinal such that $2 \leq κ\leq 2^{\…
A widely connected topological space made from diamond
Samuel M. Corson
We give the construction of an infinite topological space with unusual properties. The space is regular, separable, and connected, but removing any nonempty open set leaves the rem…
Bi-orders do not arise from total orders
Samuel M. Corson
We present some Zermelo-Fraenkel consistency results regarding bi-orderability of groups, as well as a construction of groups with Conradian orders whose every action on metric spa…
The independence of Stone's Theorem from the Boolean Prime Ideal Theorem
Samuel M. Corson
We give a permutation model in which Stone's Theorem (every metric space is paracompact) is false and the Boolean Prime Ideal Theorem (every ideal in a Boolean algebra extends to a…
A Nunke type classification in the locally compact setting
Samuel M. Corson, Olga Varghese
In this short note we prove that a group G is lcH-slender -- that is, every abstract group homomorphism from a locally compact Hausdorff topological group to G has an open kernel -…
Abstract homomorphisms from some topological groups to acylindrically hyperbolic groups
Oleg Bogopolski, Samuel M. Corson
We describe homomorphisms for which the codomain is acylindrically hyperbolic and the domain is a topological group which is either completely metrizable or loca…
Strongly bounded groups of various cardinalities
Samuel M. Corson, Saharon Shelah
Strongly bounded groups are those groups for which every action by isometries on a metric space has orbits of finite diameter. Many groups have been shown to have this property, an…
Freely indecomposable almost free groups with free abelianization
Samuel M. Corson
For certain uncountable cardinals we produce a group of cardinality which is freely indecomposable, strongly -free, and whose abelianization is free abelian of rank .…
On preservation of automatic continuity
Samuel M. Corson, Ilya Kazachkov
A group is called automatically continuous if any homomorphism from a completely metrizable or locally compact Hausdorff group to has open kernel. In this paper, we study p…
Automatic continuity of -free groups
Samuel M. Corson
We prove that groups for which every countable subgroup is free (-free groups) are n-slender, cm-slender, and lcH-slender. In particular every homomorphism from a complet…
Deeply concatenable subgroups might never be free
Samuel M. Corson, Saharon Shelah
We show that certain algebraic structures lack freeness in the absence of the axiom of choice. These include some subgroups of the Baer-Specker group and the Hawaiia…