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Large abelian normal subgroups
In this paper we study the family of finite groups with the property that every maximal abelian normal subgroup is self-centralizing. It is well known that this family contains all finite supersolvable groups, but it also contains many other groups. In fact, every finite group G is a subgroup of som...
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| Published in: | Archiv der Mathematik 2018-08, Vol.111 (2), p.113-122 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c316t-7635bff282e47b3dd26711aad770eb51656fe5fd23de8fd7f16e765706a0d3f3 |
| container_end_page | 122 |
| container_issue | 2 |
| container_start_page | 113 |
| container_title | Archiv der Mathematik |
| container_volume | 111 |
| creator | Aivazidis, S. Isaacs, I. M. |
| description | In this paper we study the family of finite groups with the property that every maximal abelian normal subgroup is self-centralizing. It is well known that this family contains all finite supersolvable groups, but it also contains many other groups. In fact, every finite group
G
is a subgroup of some member
Γ
of this family, and we show that if
G
is solvable, then
Γ
can be chosen so that every abelian normal subgroup of
G
is contained in some self-centralizing abelian normal subgroup of
Γ
. |
| doi_str_mv | 10.1007/s00013-018-1192-y |
| format | article |
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G
is a subgroup of some member
Γ
of this family, and we show that if
G
is solvable, then
Γ
can be chosen so that every abelian normal subgroup of
G
is contained in some self-centralizing abelian normal subgroup of
Γ
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G
is a subgroup of some member
Γ
of this family, and we show that if
G
is solvable, then
Γ
can be chosen so that every abelian normal subgroup of
G
is contained in some self-centralizing abelian normal subgroup of
Γ
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G
is a subgroup of some member
Γ
of this family, and we show that if
G
is solvable, then
Γ
can be chosen so that every abelian normal subgroup of
G
is contained in some self-centralizing abelian normal subgroup of
Γ
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| ispartof | Archiv der Mathematik, 2018-08, Vol.111 (2), p.113-122 |
| issn | 0003-889X 1420-8938 |
| language | eng |
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| source | Springer Link |
| subjects | Mathematics Mathematics and Statistics Subgroups |
| title | Large abelian normal subgroups |
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