منابع مشابه
Finite Simple Abelian Algebras
A finite universal algebra is called strictly simple if it is simple and has no nontrivial subalgebras. An algebra is said to be Abelian if for every term t(x, ȳ) and for all elements a, b, c̄, d̄, we have the following implication: t(a, c̄) = t(a, d̄) −→ t(b, c̄) = t(b, d̄). It is shown that every finite simple Abelian universal algebra is strictly simple. This generalizes a well known fact about Ab...
متن کاملTHE AUTOMORPHISM GROUP OF NON-ABELIAN GROUP OF ORDER p^4
Let G be a finite non-abelian group of order p^4 . In this paper we give a structure theorem for the Sylow p-subgroup, Aut_p(G) , of the automorphism group of G.
متن کاملFinite Simple Abelian Algebras Are Strictly Simple
A finite universal algebra is called strictly simple if it is simple and has no nontrivial subalgebras. An algebra is said to be Abelian if for every term t(x,y) and for all elements a, b, c, d, we have the following implication: t(a,c) = t(a,d) —> t(b,c) = t(b,d) . It is shown that every finite simple Abelian universal algebra is strictly simple. This generalizes a well-known fact about Abelia...
متن کاملWarfield invariants in Abelian group algebras
LetF be a field of characteristic p 6= 0 andG an Abelian group. For each prime q and each ordinal α we calculate in terms of G and its sections the Warfield q-invariantsWα,q(V (FG)) of the group V (FG) of all normalized units in the commutative group algebra FG when either q = p,Gt/Gp is infinite and F is perfect, orG is p-mixed. Surprisingly, these invariants do not depend on F . This supplies...
متن کاملTHE STRUCTURE OF FINITE ABELIAN p-GROUPS BY THE ORDER OF THEIR SCHUR MULTIPLIERS
A well-known result of Green [4] shows for any finite p-group G of order p^n, there is an integer t(G) , say corank(G), such that |M(G)|=p^(1/2n(n-1)-t(G)) . Classifying all finite p-groups in terms of their corank, is still an open problem. In this paper we classify all finite abelian p-groups by their coranks.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1950
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1950-0034758-3