scholarly journals GROUPS WITH THE MAXIMAL CONDITION ON NON-BFC SUBGROUPS. II

2002 ◽  
Vol 45 (3) ◽  
pp. 513-522
Author(s):  
Martyn R. Dixon ◽  
Leonid A. Kurdachenko
Keyword(s):  
Finite Groups ◽  
Conjugacy Classes ◽  
Subject Classification ◽  
Finitely Generated ◽  
Maximal Condition ◽  
Primary 20E15 ◽  
Secondary 20F16 ◽  
Finite Conjugacy

AbstractA group $G$ is called a group with boundedly finite conjugacy classes (or a BFC-group) if $G$ is finite-by-abelian. A group $G$ satisfies the maximal condition on non-BFC-subgroups if every ascending chain of non-BFC-subgroups terminates in finitely many steps. In this paper the authors obtain the structure of finitely generated soluble-by-finite groups with the maximal condition on non-BFC subgroups.AMS 2000 Mathematics subject classification: Primary 20E15. Secondary 20F16; 20F24

scholarly journals Soluble groups in which every finitely generated subgroup is finitely presented

1978 ◽  
Vol 26 (1) ◽  
pp. 115-125 ◽  
Author(s):  
J. R. J. Groves
Keyword(s):  
Subject Classification ◽  
Normal Subgroups ◽  
Finitely Generated ◽  
Maximal Condition ◽  
Soluble Groups ◽  
Image Position ◽  
Finitely Presented

AbstractThe class of finitely generated soluble coherent groups is considered. It is shown that these groups have the maximal condition on normal subgroups and can be characterized in a number of ways. In particular, they are precisely the class of finitely generated soluble groups G with the property:Subject classification (Amer. Math. Soc. (MOS) 1970): primary 20 E 15; secondary 20 F 05.

Weak Cayley tables and generalized centralizer rings of finite groups

2012 ◽  
Vol 153 (2) ◽  
pp. 281-318 ◽  
Author(s):  
STEPHEN P. HUMPHRIES ◽  
EMMA L. RODE
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Conjugacy Classes ◽  
Cayley Table ◽  
A Finite Group ◽  
Finite Conjugacy ◽  
Relationship Of ◽  
Cayley Tables ◽  
The Relationship

AbstractFor a finite group G we study certain rings (k)G called k-S-rings, one for each k ≥ 1, where (1)G is the centraliser ring Z(ℂG) of G. These rings have the property that (k+1)G determines (k)G for all k ≥ 1. We study the relationship of (2)G with the weak Cayley table of G. We show that (2)G and the weak Cayley table together determine the sizes of the derived factors of G (noting that a result of Mattarei shows that (1)G = Z(ℂG) does not). We also show that (4)G determines G for any group G with finite conjugacy classes, thus giving an answer to a question of Brauer. We give a criteria for two groups to have the same 2-S-ring and a result guaranteeing that two groups have the same weak Cayley table. Using these results we find a pair of groups of order 512 that have the same weak Cayley table, are a Brauer pair, and have the same 2-S-ring.

scholarly journals The subnormal coalescence of some classes of groups of finite rank

1973 ◽  
Vol 16 (3) ◽  
pp. 324-327 ◽  
Author(s):  
Mark Drukker ◽  
Derek J. S. Robinson ◽  
Ian Stewart
Keyword(s):  
Finite Groups ◽  
Finite Rank ◽  
Nilpotent Groups ◽  
Subnormal Subgroup ◽  
Minimal Condition ◽  
Finitely Generated ◽  
Maximal Condition ◽  
Finitely Generated Groups ◽  
Subnormal Subgroups

A class of groups forms a (subnormal) coalition class, or is (subnormally) coalescent, if wheneverHandKare subnormal -subgroups of a groupGthen their join <H, K> is also a subnormal -subgroup ofG. Among the known coalition classes are those of finite groups and polycylic groups (Wielandt [15]); groups with maximal condition for subgroups (Baer [1]); finitely generated nilpotent groups (Baer [2]); groups with maximal or minimal condition on subnormal subgroups (Robinson [8], Roseblade [11, 12]); minimax groups (Roseblade, unpublished); and any subjunctive class of finitely generated groups (Roseblade and Stonehewer [13]).

scholarly journals AN EQUIVARIANT WHITEHEAD ALGORITHM AND CONJUGACY FOR ROOTS OF DEHN TWIST AUTOMORPHISMS

2001 ◽  
Vol 44 (1) ◽  
pp. 117-141 ◽  
Author(s):  
Sava Krstić ◽  
Martin Lustig ◽  
Karen Vogtmann
Keyword(s):  
Free Group ◽  
Finite Groups ◽  
Linear Growth ◽  
Conjugacy Problem ◽  
Dehn Twist ◽  
Subject Classification ◽  
Finitely Generated ◽  
Finite Sets ◽  
Outer Automorphisms ◽  
Secondary 57M07

AbstractGiven finite sets of cyclic words $\{u_1,\dots,u_k\}$ and $\{v_1,\dots,v_k\}$ in a finitely generated free group $F$ and two finite groups $A$ and $B$ of outer automorphisms of $F$, we produce an algorithm to decide whether there is an automorphism which conjugates $A$ to $B$ and takes $u_i$ to $v_i$ for each $i$. If $A$ and $B$ are trivial, this is the classic algorithm due to Whitehead. We use this algorithm together with Cohen and Lustig’s solution to the conjugacy problem for Dehn twist automorphisms of $F$ to solve the conjugacy problem for outer automorphisms which have a power which is a Dehn twist. This settles the conjugacy problem for all automorphisms of $F$ which have linear growth.AMS 2000 Mathematics subject classification: Primary 20F32. Secondary 57M07

scholarly journals Groups with boundedly finite conjugacy classes of commutators

2018 ◽  
Vol 69 (3) ◽  
pp. 1047-1051 ◽  
Author(s):  
Gláucia Dierings ◽  
Pavel Shumyatsky
Keyword(s):  
Conjugacy Classes ◽  
Finite Conjugacy

A NOTE ON THE NUMBER OF ZEROS IN THE COLUMNS OF THE CHARACTER TABLE OF A GROUP

2012 ◽  
Vol 12 (02) ◽  
pp. 1250150 ◽  
Author(s):  
JINSHAN ZHANG ◽  
ZHENCAI SHEN ◽  
SHULIN WU
Keyword(s):  
Finite Groups ◽  
Irreducible Character ◽  
Conjugacy Classes ◽  
Character Table ◽  
Number Of Zeros

The finite groups in which every irreducible character vanishes on at most three conjugacy classes were characterized [J. Group Theory13 (2010) 799–819]. Dually, we investigate the finite groups whose columns contain a small number of zeros in the character table.

scholarly journals Some properties of the growth and of the algebraic entropy of group endomorphisms

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Anna Giordano Bruno ◽  
Pablo Spiga
Keyword(s):  
Finite Groups ◽  
Addition Theorem ◽  
Finitely Generated ◽  
Growth Type ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Algebraic Entropy ◽  
Finitely Generated Groups ◽  
Identity Automorphism ◽  
Inner Automorphisms

AbstractWe study the growth of group endomorphisms, a generalization of the classical notion of growth of finitely generated groups, which is strictly related to algebraic entropy. We prove that the inner automorphisms of a group have the same growth type and the same algebraic entropy as the identity automorphism. Moreover, we show that endomorphisms of locally finite groups cannot have intermediate growth. We also find an example showing that the Addition Theorem for algebraic entropy does not hold for endomorphisms of arbitrary groups.

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