About the differences between definitions of “Capable Group”
0
$begingroup$
I am looking for the properties of groups having "immediate Descendants", in other therm, "Capable Groups"; The problem that I fond is that "Capable Group" could have many meaning!
So, could you please help me to optimize my "bibliographical" research?
I am using data bases like Mathscinet
Thank you very much
group-theory reference-request finite-groups terminology definition
asked Dec 7 '18 at 10:11
A.MessabA.Messab
507
$endgroup$
|
show 3 more comments
0
$begingroup$
I am looking for the properties of groups having "immediate Descendants", in other therm, "Capable Groups"; The problem that I fond is that "Capable Group" could have many meaning!
So, could you please help me to optimize my "bibliographical" research?
I am using data bases like Mathscinet
Thank you very much
group-theory reference-request finite-groups terminology definition
asked Dec 7 '18 at 10:11
A.MessabA.Messab
507
$endgroup$
1
$begingroup$
Just wikipedia: In mathematics, in the realm of group theory, a group is said to be capable if it occurs as the inner automorphism group of some group. Reference: R. Baer.See also the posts on this site, e.g. here.
$endgroup$
– Dietrich Burde
Dec 7 '18 at 10:19
$begingroup$
@DietrichBurde exactly Professor, also "if it is a central factor group", and "If it has immediate descendants"...; Are these equivalent definitions? They don´t seem so!
$endgroup$
– A.Messab
Dec 7 '18 at 10:22
$begingroup$
@DietrichBurde In fact the definition you gave me and "if it is a central factor group" can be seen easily as equivalent; The real problem is with "If it has immediate descendants"!
$endgroup$
– A.Messab
Dec 7 '18 at 10:28
$begingroup$
@DietrichBurde The idea is how to restrict my research on "capable groups of the definition "If it has immediate descendants"?
$endgroup$
– A.Messab
Dec 7 '18 at 10:37
1
$begingroup$
Yes, Hall has discussed these equivalent properties in his publication "The classification of prime-power groups" of 1940, page 137. A group is capable if it has immediate descendents.
$endgroup$
– Dietrich Burde
Dec 7 '18 at 10:50
|
show 3 more comments
0
0
0
$begingroup$
I am looking for the properties of groups having "immediate Descendants", in other therm, "Capable Groups"; The problem that I fond is that "Capable Group" could have many meaning!
So, could you please help me to optimize my "bibliographical" research?
I am using data bases like Mathscinet
Thank you very much
group-theory reference-request finite-groups terminology definition
asked Dec 7 '18 at 10:11
A.MessabA.Messab
507
$endgroup$
I am looking for the properties of groups having "immediate Descendants", in other therm, "Capable Groups"; The problem that I fond is that "Capable Group" could have many meaning!
So, could you please help me to optimize my "bibliographical" research?
I am using data bases like Mathscinet
Thank you very much
group-theory reference-request finite-groups terminology definition
group-theory reference-request finite-groups terminology definition
asked Dec 7 '18 at 10:11
A.MessabA.Messab
507
asked Dec 7 '18 at 10:11
A.MessabA.Messab
507
asked Dec 7 '18 at 10:11
A.MessabA.Messab
507
asked Dec 7 '18 at 10:11
A.MessabA.Messab
507
asked Dec 7 '18 at 10:11
A.MessabA.Messab
507
507
1
$begingroup$
Just wikipedia: In mathematics, in the realm of group theory, a group is said to be capable if it occurs as the inner automorphism group of some group. Reference: R. Baer.See also the posts on this site, e.g. here.
$endgroup$
– Dietrich Burde
Dec 7 '18 at 10:19
$begingroup$
@DietrichBurde exactly Professor, also "if it is a central factor group", and "If it has immediate descendants"...; Are these equivalent definitions? They don´t seem so!
$endgroup$
– A.Messab
Dec 7 '18 at 10:22
$begingroup$
@DietrichBurde In fact the definition you gave me and "if it is a central factor group" can be seen easily as equivalent; The real problem is with "If it has immediate descendants"!
$endgroup$
– A.Messab
Dec 7 '18 at 10:28
$begingroup$
@DietrichBurde The idea is how to restrict my research on "capable groups of the definition "If it has immediate descendants"?
$endgroup$
– A.Messab
Dec 7 '18 at 10:37
1
$begingroup$
Yes, Hall has discussed these equivalent properties in his publication "The classification of prime-power groups" of 1940, page 137. A group is capable if it has immediate descendents.
$endgroup$
– Dietrich Burde
Dec 7 '18 at 10:50
|
show 3 more comments
1
$begingroup$
Just wikipedia: In mathematics, in the realm of group theory, a group is said to be capable if it occurs as the inner automorphism group of some group. Reference: R. Baer.See also the posts on this site, e.g. here.
$endgroup$
– Dietrich Burde
Dec 7 '18 at 10:19
$begingroup$
@DietrichBurde exactly Professor, also "if it is a central factor group", and "If it has immediate descendants"...; Are these equivalent definitions? They don´t seem so!
$endgroup$
– A.Messab
Dec 7 '18 at 10:22
$begingroup$
@DietrichBurde In fact the definition you gave me and "if it is a central factor group" can be seen easily as equivalent; The real problem is with "If it has immediate descendants"!
$endgroup$
– A.Messab
Dec 7 '18 at 10:28
$begingroup$
@DietrichBurde The idea is how to restrict my research on "capable groups of the definition "If it has immediate descendants"?
$endgroup$
– A.Messab
Dec 7 '18 at 10:37
1
$begingroup$
Yes, Hall has discussed these equivalent properties in his publication "The classification of prime-power groups" of 1940, page 137. A group is capable if it has immediate descendents.
$endgroup$
– Dietrich Burde
Dec 7 '18 at 10:50
1
1
$begingroup$
Just wikipedia: In mathematics, in the realm of group theory, a group is said to be capable if it occurs as the inner automorphism group of some group. Reference: R. Baer.See also the posts on this site, e.g. here.
$endgroup$
– Dietrich Burde
Dec 7 '18 at 10:19
$begingroup$
Just wikipedia: In mathematics, in the realm of group theory, a group is said to be capable if it occurs as the inner automorphism group of some group. Reference: R. Baer.See also the posts on this site, e.g. here.
$endgroup$
– Dietrich Burde
Dec 7 '18 at 10:19
$begingroup$
@DietrichBurde exactly Professor, also "if it is a central factor group", and "If it has immediate descendants"...; Are these equivalent definitions? They don´t seem so!
$endgroup$
– A.Messab
Dec 7 '18 at 10:22
$begingroup$
@DietrichBurde exactly Professor, also "if it is a central factor group", and "If it has immediate descendants"...; Are these equivalent definitions? They don´t seem so!
$endgroup$
– A.Messab
Dec 7 '18 at 10:22
$begingroup$
@DietrichBurde In fact the definition you gave me and "if it is a central factor group" can be seen easily as equivalent; The real problem is with "If it has immediate descendants"!
$endgroup$
– A.Messab
Dec 7 '18 at 10:28
$begingroup$
@DietrichBurde In fact the definition you gave me and "if it is a central factor group" can be seen easily as equivalent; The real problem is with "If it has immediate descendants"!
$endgroup$
– A.Messab
Dec 7 '18 at 10:28
$begingroup$
@DietrichBurde The idea is how to restrict my research on "capable groups of the definition "If it has immediate descendants"?
$endgroup$
– A.Messab
Dec 7 '18 at 10:37
$begingroup$
@DietrichBurde The idea is how to restrict my research on "capable groups of the definition "If it has immediate descendants"?
$endgroup$
– A.Messab
Dec 7 '18 at 10:37
1
1
$begingroup$
Yes, Hall has discussed these equivalent properties in his publication "The classification of prime-power groups" of 1940, page 137. A group is capable if it has immediate descendents.
$endgroup$
– Dietrich Burde
Dec 7 '18 at 10:50
$begingroup$
Yes, Hall has discussed these equivalent properties in his publication "The classification of prime-power groups" of 1940, page 137. A group is capable if it has immediate descendents.
$endgroup$
– Dietrich Burde
Dec 7 '18 at 10:50
|
show 3 more comments
0
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1
$begingroup$
Just wikipedia: In mathematics, in the realm of group theory, a group is said to be capable if it occurs as the inner automorphism group of some group. Reference: R. Baer.See also the posts on this site, e.g. here.
$endgroup$
– Dietrich Burde
Dec 7 '18 at 10:19
$begingroup$
@DietrichBurde exactly Professor, also "if it is a central factor group", and "If it has immediate descendants"...; Are these equivalent definitions? They don´t seem so!
$endgroup$
– A.Messab
Dec 7 '18 at 10:22
$begingroup$
@DietrichBurde In fact the definition you gave me and "if it is a central factor group" can be seen easily as equivalent; The real problem is with "If it has immediate descendants"!
$endgroup$
– A.Messab
Dec 7 '18 at 10:28
$begingroup$
@DietrichBurde The idea is how to restrict my research on "capable groups of the definition "If it has immediate descendants"?
$endgroup$
– A.Messab
Dec 7 '18 at 10:37
1
$begingroup$
Yes, Hall has discussed these equivalent properties in his publication "The classification of prime-power groups" of 1940, page 137. A group is capable if it has immediate descendents.
$endgroup$
– Dietrich Burde
Dec 7 '18 at 10:50