A new characteristic subgroup for finite 𝑝-groups

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.

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Groupes géométriques de rang de Morley fini

Journal of the Institute of Mathematics of Jussieu ◽

10.1017/s1474748008000212 ◽

2008 ◽

Vol 7 (4) ◽

pp. 751-792 ◽

Cited By ~ 3

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.

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A characteristic subgroup of Σ4-free groups

Israel Journal of Mathematics ◽

10.1007/bf02762712 ◽

1996 ◽

Vol 94 (1) ◽

pp. 367-379 ◽

Cited By ~ 8

Author(s):

Bernd Stellmacher

Keyword(s):

Free Groups ◽

Characteristic Subgroup

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FC-nilpotent and FC-soluble groups

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s030500410003139x ◽

1956 ◽

Vol 52 (3) ◽

pp. 391-398 ◽

Cited By ~ 17

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.

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A Characteristic Subgroup of a p-Stable Group

Canadian Journal of Mathematics ◽

10.4153/cjm-1968-107-2 ◽

1968 ◽

Vol 20 ◽

pp. 1101-1135 ◽

Cited By ~ 54

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.

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Automorphisms of braid groups on orientable surfaces

Journal of Knot Theory and Its Ramifications ◽

10.1142/s021821651650022x ◽

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].

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

Algebra Colloquium ◽

10.1142/s1005386713000321 ◽

2013 ◽

Vol 20 (02) ◽

pp. 349-360 ◽

Cited By ~ 6

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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