منابع مشابه
Finite Groups Embeddable in Division Rings
In [He], Herstein conjectured that odd-order subgroups of division rings K were cyclic, and he proved this to be the case when K is the division ring of the real quaternions. Herstein’s conjecture was settled negatively in [Am]. As part of his complete classification of finite groups in division rings, Amitsur showed that the smallest noncyclic odd-order group that can be embedded in a division...
متن کاملAlgorithmic Problems in Amalgams of Finite Groups
Geometric methods proposed by Stallings [53] for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups [4, 25, 37, 38, 43, 48, 56]. It turns out that Stallings’ methods can be effectively generalized for the class of amalgams of finite groups [39]. In the present paper we employ subgroup gr...
متن کاملAlgorithmic Problems in Amalgams of Finite Groups: Conjugacy and Intersection
Geometric methods proposed by Stallings [46] for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups [3, 19, 29, 30, 36, 41, 49]. In the present paper we employ the generalized Stallings’ methods, developed by the author in [32], to solve various algorithmic problems concerning finitely g...
متن کاملStallings Foldings and Subgroups of Amalgams of Finite Groups
In the 1980’s Stallings [35] showed that every finitely generated subgroup of a free group is canonically represented by a finite minimal immersion of a bouquet of circles. In terms of the theory of automata, this is a minimal finite inverse automaton. This allows for the deep algorithmic theory of finite automata and finite inverse monoids to be used to answer questions about finitely generate...
متن کاملSteinberg groups as amalgams
For any root system and any commutative ring, we give a relatively simple presentation of a group related to its Steinberg group St. This includes the case of infinite root systems used in Kac–Moody theory, for which the Steinberg group was defined by Tits and Morita–Rehmann. In most cases, our group equals St, giving a presentation with many advantages over the usual presentation of St. This e...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1972
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500001543