Showing papers in "Journal of Algebra in 1972"

TL;DR: In this paper, the authors consider the problem of finding a non-abelian free group with a solvable normal subgroup R such that R is locally finite (i.e., every jinite subset generates a $nite subgroup).

TL;DR: In this paper, it was shown that the polynomial ring over k is isomorphic to polynomials over k. This is a corollary of (3.3) and (7.7) of the present paper.

TL;DR: Hering, Kantor, and Seitz as mentioned in this paper showed that a minimal counteresamplc has a cyclic two points stabilizer, and then applied a result of Kantor and O'Nan.

TL;DR: In this article, the authors discuss the geometry and determine the automorphism group of the unital or unitary block design associated with the threedimensional unitary group, and show that the three-dimensional projective unitary groups act on X as doubly-transitive permutation groups, each member of d is the set of isotropic one-dimensional subs paces contained in a fixed nonisotropic subspace of V.

TL;DR: In this article, the Schur subgroup S(k) of the B rauer group B(K) consists of those algebra classes which contain a simple component of the group algebra kG for some finite group G. The invariants of these algebra classes are characterized by invariants, and it is reasonable to ask whether the elements of the Brauer group are distinguished by behavior of invariants.

TL;DR: In this paper, it was shown that any crystallographic Coxeter group appears as the Weyl group of some Tits' system (or (B, N)-pair) [I 1 by 1].

TL;DR: In this article, it was shown that the reverse of this situation also holds, namely, if 17 is a finite projective plane of order q2 which admits a collineation group G isomorphic to PSU,(q2), then I7is a desarguesian plane and G acts on li'in the usual manner, that is, as PSU,q) acts on PG2(q 2 ).

TL;DR: In this article, the problem of controlling subgroups of the shape O&Y,(R)) for various r-subgroups R was considered, and it was shown that the problem can be solved by restricting attention to a subset M,(A) of H(A).

TL;DR: In this paper, it was shown that every character of a finite semigroup can be expressed as an integral linear combination of characters induced from linear characters of its elementary subgroups, and that two representations of S are equivalent if and only if they are equivalent on the subgroups of S.

TL;DR: Theorem 3.1-3.3 as mentioned in this paper generalizes the result of Amitsur, Posner, Herstein, Kaplansky, and others, who showed that the central closure of a primitive ring with a minimal right ideal eA such that eAe is a finite dimensional division algebra over C can be obtained by embedding a prime ring in primitive rings.

TL;DR: The dimension subgroup conjecture has been verified for Abelian-by-cyclic groups and for split extensions of Abelian groups by groups satisfying the conjecture in this article, and the conjecture was shown to be true for the Sylow subgroups of the symmetric groups.

TL;DR: In this article, the problem of determining the conjugacy classes and corresponding centralizers of elements in affine groups is reduced to finding the semisimple and unipotent parts of an algebraically closed field.