Results 21 to 30 of about 202,613,988 (162)

Finite groups contain large centralizers

, 2021
Every finite non-abelian group of order n has a non-central element whose centralizer has order exceeding n^{1/3}. The proof does not rely on the classification of finite simple groups, yet it uses the Feit-Thompson theorem.Depto. de Álgebra, Geometría y
Palacín, Daniel, Palacín Cruz, Daniel, Daniel Palacín   +2 more
core   +1 more source

The finite simple groups have complemented subgroup lattices [PDF]

, 2004
We prove an old standing conjecture by showing that the lattice of subgroups of every finite simple group is a complemented lattice. We achieve this result by using the classification of finite simple groups, and information on the maximal ...
ZACHER, GIOVANNI, COSTANTINI, MAURO
core   +1 more source

On the number of prime order subgroups of finite groups [PDF]

, 2009
Let G be a finite group and let ?(G) be the number of prime order subgroups of G. We determine the groups G with the property ?(G)??G?/2?1, extending earlier work of C. T. C.
Scott, Stuart, Scott, S.D., Burness, Tim C, Burness, T.C.   +3 more
core   +1 more source

Endotrivial modules for finite groups of Lie type. [PDF]

, 2006
We classify the endotrivial modules for all finite groups of Lie type in defining ...
Mazza, Nadia, Nakano, Daniel, Carlson, Jon   +2 more
core   +4 more sources

Learning to be simple

AI for Science
In this work we employ machine learning to understand structured mathematical data involving finite groups and derive a theorem about necessary properties of generators of finite simple groups.
Yang-Hui He, Vishnu Jejjala, Mishra Challenger, Em Sharnoff   +3 more
doaj   +1 more source

Totally -closed finite groups with trivial Fitting subgroup

Bulletin of Mathematical Sciences
A finite permutation group [Formula: see text] is called [Formula: see text]-closed if [Formula: see text] is the largest subgroup of [Formula: see text] which leaves invariant each of the [Formula: see text]-orbits for the induced action on [Formula ...
Majid Arezoomand, Mohammad A. Iranmanesh, Cheryl E. Praeger, Gareth Tracey   +3 more
doaj   +1 more source

Blocks with extra-special defect groups of finite quasi-simple groups [PDF]

, 2011
The classification of blocks with special defect groups is one of the main problems in the modular representations theory. In work on nilpotent and controlled blocks of finite quasi-simple groups, we notice that blocks with extra-special defect groups ...
An, Jianbei, Jianbei An, Eaton, Charles W.; id_orcid, Eaton, CW, Charles W. Eaton, An, J   +5 more
core   +1 more source

A complete classification of shuffle groups

Forum of Mathematics, Sigma
For positive integers k and n, the shuffle group $G_{k,kn}$ is generated by the $k!$ permutations of a deck of $kn$ cards performed by cutting the deck into k piles with n cards in each pile, and then perfectly interleaving these ...
Binzhou Xia, Junyang Zhang, Zhishuo Zhang, Wenying Zhu   +3 more
doaj   +1 more source

A brief history of the classification of the finite simple groups [PDF]

Bulletin of the American Mathematical Society, 2001
We present some highlights of the 110-year project to classify the finite simple groups.
openaire   +3 more sources

Criteria for classifying prime graphs of PSL(2,

Journal of Computational Algebra
For a finite group G , the prime graph Γ ( G ) (also known as Gruenberg-Kegel graph) is defined to be the graph where the vertices are the primes that divide | G | such that two vertices p and q share an edge if and only if there is an element of order ...
Thomas Michael Keller, Zachary Martin, Alexa Renner, Gabriel Roca, Eric Yu   +4 more
doaj   +1 more source