scholarly journals Generalized Iterated Wreath Products of Symmetric Groups and Generalized Rooted Trees Correspondence

2018 ◽  
pp. 29-46
Author(s):  
Mee Seong Im ◽  
Angela Wu
Keyword(s):  
Symmetric Groups ◽  
Wreath Products ◽  
Rooted Trees

CONJUGATION IN TREE AUTOMORPHISM GROUPS

2001 ◽  
Vol 11 (05) ◽  
pp. 529-547 ◽  
Author(s):  
PIOTR W. GAWRON ◽  
VOLODYMYR V. NEKRASHEVYCH ◽  
VITALY I. SUSHCHANSKY
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Rooted Tree ◽  
Symmetric Groups ◽  
Wreath Products ◽  
Rooted Trees ◽  
Full Description ◽  
Finite Tree ◽  
Locally Finite ◽  
Infinite Sequences

It is given a full description of conjugacy classes in the automorphism group of the locally finite tree and of a rooted tree. They are characterized by their types (a labeled rooted trees) similar to the cyclical types of permutations. We discuss separately the case of a level homogenous tree, i.e. conjugality in wreath products of infinite sequences of symmetric groups. It is proved those automorphism groups of rooted and homogenous non-rooted trees are ambivalent.

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.

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