scholarly journals The permutation enumeration of wreath products Ck§Sn of cyclic and symmetric groups

2003 ◽  
Vol 30 (1-2) ◽  
pp. 343-368 ◽  
Author(s):  
Jennifer D. Wagner
Keyword(s):  
Symmetric Groups ◽  
Wreath Products ◽  
Permutation Enumeration

scholarly journals SYMMETRIC GROUPS, WREATH PRODUCTS, MORITA EQUIVALENCES, AND BROUÉ'S ABELIAN DEFECT GROUP CONJECTURE

2002 ◽  
Vol 34 (2) ◽  
pp. 174-185 ◽  
Author(s):  
JOSEPH CHUANG ◽  
RADHA KESSAR
Keyword(s):  
Symmetric Groups ◽  
Wreath Products ◽  
Defect Group ◽  
Negative Integer ◽  
Morita Equivalent

It is shown that for any prime p, and any non-negative integer w less than p, there exist p-blocks of symmetric groups of defect w, which are Morita equivalent to the principal p-block of the group Sp [rmoust ] Sw. Combined with work of J. Rickard, this proves that Broué's abelian defect group conjecture holds for p-blocks of symmetric groups of defect at most 5.

scholarly journals On the minimal ramification problem for ℓ-groups

2010 ◽  
Vol 146 (3) ◽  
pp. 599-606 ◽  
Author(s):  
Hershy Kisilevsky ◽  
Jack Sonn
Keyword(s):  
Galois Group ◽  
Prime Number ◽  
Finite Fields ◽  
Symmetric Groups ◽  
Wreath Products ◽  
The Other ◽  
Classical Groups ◽  
Direct Products ◽  
Cyclic Groups ◽  
Other Hand

AbstractLet ℓ be a prime number. It is not known whether every finite ℓ-group of rank n≥1 can be realized as a Galois group over ${\Bbb Q}$ with no more than n ramified primes. We prove that this can be done for the (minimal) family of finite ℓ-groups which contains all the cyclic groups of ℓ-power order and is closed under direct products, (regular) wreath products and rank-preserving homomorphic images. This family contains the Sylow ℓ-subgroups of the symmetric groups and of the classical groups over finite fields of characteristic not ℓ. On the other hand, it does not contain all finite ℓ-groups.

scholarly journals Automorphism Groups of Rational Circulant Graphs

10.37236/2039 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Mikhail Klin ◽  
István Kovács
Keyword(s):  
Orthogonal Group ◽  
Automorphism Groups ◽  
Cayley Graphs ◽  
Symmetric Groups ◽  
Wreath Products ◽  
Circulant Graphs ◽  
Cyclic Groups ◽  
Block Structures

The paper concerns the automorphism groups of Cayley graphs over cyclic groups which have a rational spectrum (rational circulant graphs for short). With the aid of the techniques of Schur rings it is shown that the problem is equivalent to consider the automorphism groups of orthogonal group block structures of cyclic groups. Using this observation, the required groups are expressed in terms of generalized wreath products of symmetric groups.

scholarly journals Character correspondences for symmetric groups and wreath products

2017 ◽  
Vol 29 (3) ◽  
Author(s):  
Anton Evseev
Keyword(s):  
Finite Group ◽  
Symmetric Groups ◽  
Wreath Products ◽  
Irreducible Characters ◽  
Arbitrary Finite Group

AbstractThe Alperin–McKay conjecture relates irreducible characters of a block of an arbitrary finite group to those of its

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