A new characteristic subgroup for finite 𝑝-groups

2021 ◽  
Author(s):  
Paul Flavell ◽  
Bernd Stellmacher
Keyword(s):  
Characteristic Subgroup

A characteristic subgroup ofN-stable groups

1986 ◽  
Vol 54 (1) ◽  
pp. 51-59 ◽  
Author(s):  
M. Dolores Perez-Ramos
Keyword(s):  
Characteristic Subgroup

scholarly journals Correction to: “A characteristic subgroup of a group of odd order”

1975 ◽  
Vol 61 (2) ◽  
pp. 607-607b
Author(s):  
Zvi Arad ◽  
George Glauberman
Keyword(s):  
Characteristic Subgroup ◽  
Odd Order

scholarly journals p-Groups with a unique proper non-trivial characteristic subgroup

2011 ◽  
Vol 348 (1) ◽  
pp. 85-109 ◽  
Author(s):  
S.P. Glasby ◽  
P.P. Pálfy ◽  
Csaba Schneider
Keyword(s):  
Characteristic Subgroup

In vivo and in vitro activity of neutrophil alkaline phosphatase in acute myelocytic leukemia with 8;21 translocation

Blood ◽  
1981 ◽  
Vol 58 (6) ◽  
pp. 1213-1217
Author(s):  
N Kamada ◽  
H Dohy ◽  
K Okada ◽  
N Oguma ◽  
A Kuramoto ◽  
...  
Keyword(s):  
Alkaline Phosphatase ◽  
Genetic Alterations ◽  
Leukemic Cells ◽  
Characteristic Subgroup ◽  
Acute Myelocytic Leukemia ◽  
Myelocytic Leukemia ◽  
Fab Classification ◽  
Neutrophil Alkaline Phosphatase

Cytogenetic studies were made on 160 patients with acute nonlymphocytic leukemia (ANLL) between 1963 and 1979, of whom 115 had acute myelocytic leukemia with 67 patients showing aneuploidy (58.3%). Among these, 24 patients were found to have similar chromosome alterations that appeared to involve specifically chromosomes 8 and 21. Banding studies on at least 7 of these patients confirmed the presence of a translocation between these two chromosomes. Of 160 ANLL patients, 142 were scored for neutrophil alkaline phosphatase (neutrophil AP) at the time of diagnosis. Fifty-nine patients showed a low neutrophil AP score, 42 a normal value, and 41 a high value. All patients with 8;21 (or C/G) translocation had a low neutrophil AP score and leukemic cells with maturation (M2 of FAB classification) in the bone marrow. In vitro liquid culture for 2 wk of 8;21 translocated leukemic cells revealed no increase of neutrophil AP activity nor increase of mature granulocytes, whereas 9;22 translocated chronic myelocytic leukemia cells with a low neutrophil AP score did so. Neutrophil AP score at the time of diagnosis in acute myelocytic leukemia is very useful for detecting 8;21 translocation AML and for studying the pathophysiology and genetic alterations of the characteristic subgroup of AML with 8′21 translocation.

Groupes géométriques de rang de Morley fini

2008 ◽  
Vol 7 (4) ◽  
pp. 751-792 ◽  
Author(s):  
Olivier Frécon
Keyword(s):  
Normal Subgroup ◽  
Large Class ◽  
Quotient Group ◽  
Characteristic Subgroup ◽  
Morley Rank ◽  
Connected Group ◽  
Finite Morley Rank ◽  
Linearity Conjecture

AbstractWe consider a new subgroup In(G) in any group G of finite Morley rank. This definably characteristic subgroup is the smallest normal subgroup of G from which we can hope to build a geometry over the quotient group G/ In(G). We say that G is a geometric group if In(G) is trivial.This paper is a discussion of a conjecture which states that every geometric group G of finite Morley rank is definably linear over a ring K1 ⊕…⊕ Kn where K1,…,Kn are some interpretable fields. This linearity conjecture seems to generalize the Cherlin–Zil'ber conjecture in a very large class of groups of finite Morley rank.We show that, if this linearity conjecture is true, then there is a Rosenlicht theorem for groups of finite Morley rank, in the sense that the quotient group of any connected group of finite Morley rank by its hypercentre is definably linear.

A characteristic subgroup of Σ4-free groups

1996 ◽  
Vol 94 (1) ◽  
pp. 367-379 ◽  
Author(s):  
Bernd Stellmacher
Keyword(s):  
Free Groups ◽  
Characteristic Subgroup

FC-nilpotent and FC-soluble groups

1956 ◽  
Vol 52 (3) ◽  
pp. 391-398 ◽  
Author(s):  
A. M. Duguid ◽  
D. H. McLain
Keyword(s):  
Finite Number ◽  
Finite Groups ◽  
Abelian Groups ◽  
Characteristic Subgroup ◽  
Arbitrary Group ◽  
Soluble Groups ◽  
Image Position

Let an element of a group be called an FC element if it has only a finite number of conjugates in the group. Baer(1) and Neumann (8) have discussed groups in which every element is FC, and called them FC-groups. Both Abelian and finite groups are trivially FC-groups; Neumann has studied the properties common to FC-groups and Abelian groups, and Baer the properties common to FC-groups and finite groups. Baer has also shown that, for an arbitrary group G, the set H1 of all FC elements is a characteristic subgroup. Haimo (3) has defined the FC-chain of a group G byHi/Hi−1 is the subgroup of all FC elements in G/Hi−1.

A Characteristic Subgroup of a p-Stable Group

1968 ◽  
Vol 20 ◽  
pp. 1101-1135 ◽  
Author(s):  
George Glauberman
Keyword(s):  
Finite Group ◽  
Characteristic Subgroup ◽  
Stable Group ◽  
A Finite Group

Let p be a prime, and let S be a Sylow p-subgroup of a finite group G. J. Thompson (13; 14) has introduced a characteristic subgroup JR(S) and has proved the following results:(1.1) Suppose that p is odd. Then G has a normal p-complement if and only if C(Z(S)) and N(JR(S)) have normal p-complements.

scholarly journals Automorphisms of braid groups on orientable surfaces

2016 ◽  
Vol 25 (05) ◽  
pp. 1650022
Author(s):  
Byung Hee An
Keyword(s):  
Mapping Class Group ◽  
Class Group ◽  
Automorphism Groups ◽  
Orientable Surface ◽  
Braid Groups ◽  
Mapping Class ◽  
Characteristic Subgroup ◽  
Group Extensions ◽  
Extended Mapping ◽  
Orientable Surfaces

In this paper, we compute the automorphism groups [Formula: see text] and [Formula: see text] of braid groups [Formula: see text] and [Formula: see text] on every orientable surface [Formula: see text], which are isomorphic to group extensions of the extended mapping class group [Formula: see text] by the transvection subgroup except for a few cases. We also prove that [Formula: see text] is always a characteristic subgroup of [Formula: see text], unless [Formula: see text] is a twice-punctured sphere and [Formula: see text].

On the Intersection of the Normalizers of the Nilpotent Residuals of All Subgroups of a Finite Group

2013 ◽  
Vol 20 (02) ◽  
pp. 349-360 ◽  
Author(s):  
Lü Gong ◽  
Xiuyun Guo
Keyword(s):  
Finite Group ◽  
Characteristic Subgroup ◽  
A Finite Group ◽  
The Relationship

In this paper, a characteristic subgroup [Formula: see text] of a finite group G is defined, which is the intersection of the normalizers of the nilpotent residuals of all subgroups of G, and the properties of [Formula: see text] and the relationship between [Formula: see text] and the group G are investigated.

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