Results 231 to 240 of about 1,371,090 (265)

On a Class of Supersoluble Groups

Southeast Asian Bulletin of Mathematics, 2003
It is well known that the product of two normal supersoluble subgroups need not be supersoluble in general. The author considers a class \(\mathfrak C\) of groups \(G\) which contain a normal subgroup \(N\) such that for some positive integer \(n\) every subgroup of the \(n\)th term of the lower central series of \(G/N'\) is normal in \(G/N'\).
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Quotient Groups of Groups of Certain Classes

Ukrainian Mathematical Journal, 2000
Summary: For an arbitrary variety \(\mathfrak X\) of groups and an arbitrary class \(\mathfrak Y\) of groups that is closed under quotient groups we prove that a quotient group \(G/N\) of the group \(G\) possesses an invariant system with \(\mathfrak X\)- and \(\mathfrak Y\)-factors (respectively, is residually a \(\mathfrak Y\)-group) if \(G ...
Chernikov, N. S., Trebenko, D. Ya.
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CLASS NUMBERS AND GROUPS OF ALGEBRAIC GROUPS

Mathematics of the USSR-Izvestiya, 1980
The class number of an algebraic group G defined over a global field is the number of double cosets of the adele group GA with respect to the subgroups of integral and principal adeles. In most cases the set of double cosets has the natural structure of an abelian group, called the class group of G.
Platonov, V. P., Bondarenko, A. A., Rapinchuk, A. S.   +2 more
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Minimal classes and maximal class inp-groups

Israel Journal of Mathematics, 1999
The authors study finite non-commutative \(p\)-groups \(G\) with the property that the number of minimal classes (i.e., the smallest non-singleton conjugacy classes) is \(p-1\). Among others, they prove the following results. For such a group, \(Z_2(G)\) is an elementary Abelian \(p\)-group, \(|Z_2(G):Z(G)|=p\) and the minimal classes are exactly the ...
LONGOBARDI, Patrizia, MAJ, Mercede, A. MANN   +2 more
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ON A CLASS OF CYCLICALLY PRESENTED GROUPS

International Journal of Algebra and Computation, 2004
This paper considers the problem for what n and ω is the cyclically presented group Gn(ω) irreducible and trivial and studies the case when [Formula: see text] and n≥5.
Martin Edjvet, Paul Hammond
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From Class Groups to Class Fields

1999
Since the first printing of the book [35] by H. Zassenhaus and the author in 1989 algorithmic algebraic number theory has attracted rapidly increasing interest. This is documented, for example, by a regular meeting ANTS (algebraic number theory symposium) every two years whose proceedings [1], [6] give a good survey about ongoing research.
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On the automorphism of a class of groups.

2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Ideal Class Group and the Unit Group

1977
Recall that the ideal class group of a number ring R consists of equivalence classes of nonzero ideals under the relation $$ I\sim J\quad iff\quad \alpha I = \beta J\quad for{\text{ }}some{\text{ }}non{\text{ }}zero{\text{ }}\alpha ,\beta \in R; $$ the group operation is multiplication defined in the obvious way, and the fact that this is ...
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Selmer groups and ideal class groups

Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1993
The author proves bounds on the rank of an elliptic curve over an arbitrary number field \(k\) containing the cube roots of unity, in case the curve has a rational point of order 3. The bound involves the degree of \(k\), and the difference between the class group of \(k\) and part of the class group of the field \(K\) obtained by adjoining the ...
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Class-group and class-number

1979
Ian Stewart, David Tall
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