Search results

...'''' (where ''X'' is some property of groups) if it "can be recovered from groups with property ''X''". * Residually [[solvable group|solvable]] ...

...contains a [[normal subgroup]] whose corresponding [[quotient group]] is a solvable group. ...</math>-power order. Therefore, <math>\text{Gal}(L/\mathbf{Q}_p)</math> is solvable.<ref>{{citation|last=Boston|first=Nigel|title=The Proof of Fermat's Last Th ...

...t1=Brauer |first1=Richard D. |year=1963 |chapter=Representations of finite groups |title=Lectures in Mathematics |volume=1 |publisher=Wiley | pages=133–175 | ...bgroups]], called the [[Modular representation theory#Defect groups|defect groups]] of <math>B</math>. The set of irreducible characters belonging to <math>B ...

* <math>{\mathfrak g}_{2.1}</math>, [[solvable group|solvable]] <math>\mathfrak{aff}(1)=\left\{\begin{pmatrix} a&b \\ 0&0 \end{pmatrix}\, * <math>{\mathfrak g}_{2.1}\oplus {\mathfrak g}_1 </math>, decomposable solvable, Bianchi III; ...

...t2=Lucchini |first2=A. |date=1995-11-15 |title=Generation of Almost Simple Groups |url=https://www.sciencedirect.com/science/article/pii/S0021869385713452 |j * Trivially, non-abelian simple groups and the full group of automorphisms are almost simple. For <math>n=5</math> ...

...alizer functors play a major role in the [[classification of finite simple groups]]. ...le]], then the signalizer functor <math>\theta</math> itself is said to be solvable. ...

{{about|graphs defined from finite groups|other uses|Glossary of graph theory#prime}} ...eory)|tree]], it has at most eight vertices, and at most four for solvable groups.{{r|tree}} ...

==Solvable septics== ...e an example of an irreducible but solvable septic, one can generalize the solvable [[de Moivre]] [[quintic]] to get, ...

...rtation ''Il Prime Graph dei gruppi finiti'' [''the prime graphs of finite groups''], supervised by Napolitani and co-advised by Carlo Casolo.{{r|sum|mg}} ...[[Diameter (graph theory)|diameter]] at most five, and at most three for [[solvable group]]s.{{r|diam}} ...

| chapter = Number theoretical investigations on groups of finite order ...the structure of the [[Modular representation theory#Defect_groups|defect groups]] of <math>B</math>. ...

...'i''</sub> for each ''i'' between 1 and ''k''. The [[Mathieu group|Mathieu groups]] are important examples. ==Classifications of 2-transitive groups == ...

}}</ref> as well as in [[harmonic analysis]] on Lie groups and [[mathematical physics]]. ...] initially constructed for [[nilpotent group]]s to more general case of [[solvable group]]s as well.<ref>{{cite journal ...

{{Short description|Collection of groups}} ...oup|commutativity]]). Since [[set theory]] does not admit the "set of all groups", it is necessary to work with the more general concept of ''[[Class_(set_t ...

...s uniqueness results in the [[odd order theorem]] to [[group (mathematics)|groups]] with dihedral Sylow 2-subgroups. *[[p-solvable group|''p''-solvable group]] ...

...uintics|Cayley resolvent]] is a resolvent for the maximal [[Solvable group|solvable]] Galois group in degree five. It is a polynomial of [[degree of a polynomi ...equation over the [[field (mathematics)|field]] generated by this root is solvable. ...

...ular representation theory|Brauer block]] and the structure of its defect groups. It was formulated by [[Richard Brauer]] in 1955. ...bgroups]], called the [[Modular representation theory#Defect_groups|defect groups]] of <math>B</math>. The set of irreducible characters belonging to <math>B ...

...algebra]] and [[finite geometry]], the '''list of transitive finite linear groups''' is an important classification of certain highly symmetric [[Group actio ...vides a complete <!-- and irredundant? --> list of the finite 2-transitive groups whose socle is [[elementary abelian group|elementary abelian]]. ...

...f [[Hall subgroup]]s and [[Carter subgroup]]s of [[finite group|finite]] [[solvable group]]s. ...roup|''p''-groups]] for a [[prime number|prime]] ''p'', the formation of π-groups for a set of primes π, and the formation of [[nilpotent group]]s. ...

...general conjecture for any prime value of <math>p</math> and more general groups. ...last=McKay |first=John |date=1971 |title=A new invariant for finite simple groups|volume=128 |journal=[[Notices of the American Mathematical Society]] |pages ...

...cretely realize these automorphisms in the matrix representations of these groups. For <math>A_n = \mathfrak{sl}(n+1, \mathbb{C})</math>, the automorphism ca ...h>, where <math>\mathfrak{g}_{\alpha}</math> are root spaces, is a maximal solvable subalgebra (that is, a [[Borel subalgebra]]).<ref>{{harvnb|Serre|2000|loc=C ...