...d group]]; a group with no non-trival [[abelian group|abelian]] [[quotient group|quotient]].
* Joseph J. Rotman, ''Advanced Modern Algebra'', Graduate studies in mathematics '''114''', American Mathematical Society (2010) {{ISBN|0-8218-4741-4}}
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...ves as a synonym for the concepts of "finite mathematics" and "discrete mathematics" .
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...rder 8 is the smallest finite group that is not a T-group. A group is a T-group if and only if it is equal to its own [[Wielandt subgroup]].
* Derek Robinson, "A Course in the Theory of Groups", Graduate Texts in Mathematics '''80''' Springer (1996) {{ISBN|0-387-94461-3}} {{ZBL|0483.20001}}
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A group which is a [[direct product]] of [[simple group]]s.
* Derek Robinson, "A Course in the Theory of Groups", Graduate Texts in Mathematics '''80''' Springer (1996) {{ISBN|0-387-94461-3}} {{ZBL|0483.20001}}
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An example of an infinite [[Abelian group]] which is a building block in the structure theory of such groups.
...}$. Reinhold Baer proved in 1937 that $\mathcal{B}$ is not [[Free Abelian group|free abelian]], whereas Specker proved in 1950 that every countable subgrou
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...$ and its centralizer $K$ in $G$; indeed $K$ is isomorphic to the quotient group $G/B$.
...form space]] with respect to the [[uniformity]] implied by the topological group structure.
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A [[subgroup]] that determines much of the structure of its containing group. The concept may be generalized to [[essential submodule]]s.
A [[subgroup]] $S$ of a (typically [[abelian group|abelian]]) [[group]] $G$ is said to be ''essential'' if whenever $H$ is a non-trivial subgro
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...term "continuous group" often stands for [[Topological group|topological group]] [[#References|[2]]].
...R><TD valign="top">[3]</TD> <TD valign="top"> N. Bourbaki, "Elements of mathematics. Lie groups and Lie algebras" , Addison-Wesley (1975) (Translated from Fr
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...odule. The completion $\hat A$ of the module $A$ as an Abelian topological group can be given the natural structure of a topological module over the complet
...al $G$-module, where $G$ is a topological group, is an Abelian topological group $A$ that is a $G$-module, where the multiplication mapping $G \times A \to
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...Lie transformation group]]; [[Algebraic group of transformations|Algebraic group of transformations]]).
...ms" A.D. Aleksandrov (ed.) A.N. Kolmogorov (ed.) M.A. Lavrent'ev (ed.) , ''Mathematics, its content, methods and meaning'' , '''3''' , Amer. Math. Soc. (1962) pp.
2 KB (330 words) - 09:46, 11 August 2014
The adjoint group of a linear group $G$ is
...hop{\textrm{Ad}}} \Ad G$ which is the image of the Lie group or algebraic group $G$ under the adjoint representation (cf.
2 KB (278 words) - 17:24, 20 January 2022
...uch rings (cf. [[Dedekind ring]]). The [[invertible element]]s of the semi-group $\mathfrak A$ are said to be invertible ideals. Each invertible ideal has a
<TR><TD valign="top">[2]</TD> <TD valign="top"> N. Bourbaki, "Elements of mathematics. Commutative algebra" , Addison-Wesley (1972) (Translated from French)</T
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...ement $g \in G$ will be the [[centralizer]] of this element in $G$; if the group acts by conjugation on the set of its subgroups, then the stabilizer of a s
...ean motions, then the isotropy subgroup $G_m$ of $m \in M$ is the symmetry group of the structure $m \in M$.
2 KB (288 words) - 16:36, 1 May 2016
$#C+1 = 62 : ~/encyclopedia/old_files/data/O070/O.0700120 Ordered group
A [[Group|group]] $ G $
5 KB (742 words) - 16:40, 31 March 2020
$#C+1 = 10 : ~/encyclopedia/old_files/data/S084/S.0804920 Shmidt group
...nt group|Nilpotent group]]). A Shmidt group is a [[Solvable group|solvable group]] of order $ p ^ \alpha q ^ \beta $,
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$#C+1 = 13 : ~/encyclopedia/old_files/data/L058/L.0508600 Lie group, Banach
endowed with a group structure and an analytic Banach manifold structure (cf. [[Banach analytic
3 KB (427 words) - 22:16, 5 June 2020
The automorphism group of a
group of all automorphisms of the field $L$ leaving the elements of
3 KB (494 words) - 21:56, 5 March 2012
''in the sense of Gromov, Gromov hyperbolic group''
A [[Group|group]] $G$ with a finite generating subset $S$ for which there is some constant
3 KB (519 words) - 09:13, 6 September 2014
The ''complexification of a Lie group $G$ over $\R$'' is
a complex Lie group $G_\C$ containing $G$ as a real Lie subgroup such that the Lie algebra $\de
3 KB (501 words) - 15:05, 13 April 2024
See also: [[Baer semi-group]].
* Tsit-Yuen Lam, "Lectures on Modules and Rings" Graduate Texts in Mathematics '''189''' Springer (2012) {{ISBN|1461205255}} {{ZBL|0911.16001}}
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