Infinite Group Theory

10.1142/10354 ◽  
2016 ◽  
Author(s):  
Paul Baginski ◽  
Benjamin Fine ◽  
Anthony M Gaglione
Keyword(s):  
Group Theory ◽  
Infinite Group

Topics in Infinite Group Theory

2021 ◽  
Author(s):  
Benjamin Fine ◽  
Anja Moldenhauer ◽  
Gerhard Rosenberger ◽  
Leonard Wienke
Keyword(s):  
Group Theory ◽  
Infinite Group

scholarly journals A Compendium of Infinite Group Theory: Part 1—Countable Recognizability

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2366
Author(s):  
Francesco de Giovanni ◽  
Marco Trombetti
Keyword(s):  
Group Theory ◽  
Infinite Group ◽  
Survey Papers ◽  
Large Groups

Countably recognizable group classes were introduced by Reinhold Baer and provide a very ingenious way to study large groups through the properties of their countable subgroups. This is the reason we have chosen the countable recognizability to start this series of survey papers on infinite group theory.

Some open problems in infinite group theory

2001 ◽  
Vol 21 (5) ◽  
Author(s):  
Gerhard Rosenberger ◽  
Benjamin Fine
Keyword(s):  
Group Theory ◽  
Infinite Group ◽  
Open Problems

scholarly journals On groups of finite height

1979 ◽  
Vol 28 (1) ◽  
pp. 87-99 ◽  
Author(s):  
Stephen J. Pride
Keyword(s):  
Group Theory ◽  
Partial Order ◽  
Infinite Group ◽  
Subject Classification ◽  
Infinite Groups ◽  
Finiteness Conditions ◽  
Finite Height

AbstractIn a previous paper, ‘The concept of “largeness” in group theory’, a partial order was defined on the class of infinite groups, and this partial order was seen to give some precision to our intuitive notions of what it means for one infinite group to be ‘larger’ than another. The aim of this paper is to look more closely at groups which are ‘low down’ in this partial order, and to examine the interplay between properties of groups and finiteness conditions in group theory.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 20 E 15, 20 F 15, 20 K 10, 20 K 25; secondary 20 E 10.

scholarly journals On normally embedded subgroups of locally soluble FC-groups

1986 ◽  
Vol 28 (2) ◽  
pp. 153-159 ◽  
Author(s):  
J. C. Beidleman ◽  
M. J. Karbe
Keyword(s):  
Finite Group ◽  
Group Theory ◽  
Normal Subgroup ◽  
Sylow Subgroup ◽  
Infinite Group ◽  
Considerable Importance ◽  
Soluble Groups ◽  
Sylow Subgroups ◽  
Group A ◽  
A Finite Group

In his Habilitationsschrift [3] B. Fischer introduced the concept of a normally embedded subgroup of a finite group. A subgroup of a finite group G is said to be normally embedded in G if each of its Sylow subgroups is a Sylow subgroup of a normal subgroup of G. Meanwhile this concept has become of considerable importance in the theory of finite soluble groups and has been studied by various authors. However, in infinite group theory, normally embedded subgroups seem to have received little attention. The object of this note is to study normally embedded subgroups of locally soluble FC-groups.

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