Groups of prime-power order with a small second derived quotient

Csaba Schneider

doi:10.1016/S0021-8693(03)00294-1

Groups of prime-power order with a small second derived quotient

Csaba Schneider^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

For odd primes we prove some structure theorems for finite p-groups G, such that G″ ≠ 1 and G′/G″ = p³. Building on results of Blackburn and Hall, it is shown that γ₃(G) is a maximal subgroup of G′, the group G has a central decomposition into two simpler subgroups, and, moreover, G′ has one of two isomorphism types.

Original language	English
Pages (from-to)	539-551
Number of pages	13
Journal	Journal of Algebra
Volume	266
Issue number	2
DOIs	https://doi.org/10.1016/S0021-8693(03)00294-1
Publication status	Published - 15 Aug 2003
Externally published	Yes

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10.1016/S0021-8693(03)00294-1

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title = "Groups of prime-power order with a small second derived quotient",

abstract = "For odd primes we prove some structure theorems for finite p-groups G, such that G″ ≠ 1 and G′/G″ = p3. Building on results of Blackburn and Hall, it is shown that γ3(G) is a maximal subgroup of G′, the group G has a central decomposition into two simpler subgroups, and, moreover, G′ has one of two isomorphism types.",

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T1 - Groups of prime-power order with a small second derived quotient

AU - Schneider, Csaba

PY - 2003/8/15

Y1 - 2003/8/15

N2 - For odd primes we prove some structure theorems for finite p-groups G, such that G″ ≠ 1 and G′/G″ = p3. Building on results of Blackburn and Hall, it is shown that γ3(G) is a maximal subgroup of G′, the group G has a central decomposition into two simpler subgroups, and, moreover, G′ has one of two isomorphism types.

AB - For odd primes we prove some structure theorems for finite p-groups G, such that G″ ≠ 1 and G′/G″ = p3. Building on results of Blackburn and Hall, it is shown that γ3(G) is a maximal subgroup of G′, the group G has a central decomposition into two simpler subgroups, and, moreover, G′ has one of two isomorphism types.

KW - Derived subgroup

KW - Finite p-groups

KW - Second derived subgroup

UR - http://www.scopus.com/inward/record.url?scp=0042157281&partnerID=8YFLogxK

U2 - 10.1016/S0021-8693(03)00294-1

DO - 10.1016/S0021-8693(03)00294-1

M3 - Article

SN - 0021-8693

VL - 266

SP - 539

EP - 551

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Groups of prime-power order with a small second derived quotient

Abstract

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