Some unsolvable conjectures in finite \(p\)-groups (Q2080925)

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scientific article; zbMATH DE number 7599899

Language	Label	Description	Also known as
English	Some unsolvable conjectures in finite \(p\)-groups	scientific article; zbMATH DE number 7599899

Statements

scholarly article

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Some unsolvable conjectures in finite \(p\)-groups (English)

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Frontiers of Mathematics in China

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publication date

12 October 2022

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zbMATH Keywords

finite \(p\)-groups

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Hua-Tuan conjecture

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Higman conjecture

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Oliver conjecture

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Wiegold conjecture

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describes a project that uses

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MaRDI profile type

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full work available at URL

https://doi.org/10.1007/s11464-022-1001-6

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Finite \(p\)-groups of class 2 have noninner automorphisms of order \(p\).

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Powerful \(p\)-groups have non-inner automorphisms of order \(p\) and some cohomology.

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Finite \(p\)-groups of class 3 have noninner automorphisms of order \(p\).

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On a Special Class of Regular p-Groups

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Large Abelian Subgroups of p-Groups

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SOME PROPERTIES OF SEMI-ABELIAN -GROUPS

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On a nonregular \(p\)-group

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On the Number of Subgroups of Given Order in a Finite p-Group of Exponent p

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Groups of prime power order. Vol. 1.

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Groups of prime power order. Vol. 2.

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Groups of prime power order. Vol. 3.

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Groups of prime power order. Vol. 5.

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Groups of prime power order. Vol. 6.

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On the existence of a noninner automorphism of order \(p\) for \(p\)-groups.

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On the orders of automorphism groups of finite groups. II

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Class and Breadth of a Finite <i>p</i> -Group

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The nilpotency class of \(p\)-groups in which subgroups have few conjugates.

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Noninner automorphisms of order \(p\) of finite \(p\)-groups

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Non-PORC behaviour of a class of descendant \(p\)-groups.

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The class-breadth conjecture revisited.

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Higman's PORC conjecture for a family of groups

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A Note on the Automorphism Group of a p-Group

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Space Groups and Groups of Prime-Power Order IV. Counterexamples to the Class-Breadth Conjecture

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Noninner automorphisms of order \(p\) in finite \(p\)-groups of coclass 2, when \(p>2\).

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On the breadth of a finite p-group

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Nichtabelsche p-Gruppen besitzen äußere p-Automorphismen

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Groups of prime power order with many conjugacy classes

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Large Abelian subgroups of finite \(p\)-groups

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Abelian subgroups of small index in finite p-groups

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Existence of normal subgroups in finite \(p\)-groups.

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A partial analogue of Borel's fixed point theorem for finite \(p\)-groups.

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\(p\)-groups with maximal elementary Abelian subgroups of rank 2.

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FINITE -GROUPS WITH SMALL AUTOMORPHISM GROUP

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On Oliver's \(p\)-group conjecture.

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On Oliver's \(p\)-group conjecture. II.

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On a strong form of Oliver's \(p\)-group conjecture.

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Weak closure and Oliver's \(p\)-group conjecture.

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Enumerating <i>p</i> -Groups. I: Inequalities

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Enumerating <i>p</i> -Groups, II: Problems Whose Solution is <i>PORC</i>

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Partial Difference Sets

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ON THE EXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER TWO IN FINITE 2-GROUPS

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Finite nonabelian \(2\)-groups all of whose minimal nonabelian subgroups are metacyclic and have exponent \(4\).

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Finite \(p\)-groups with many minimal nonabelian subgroups.

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Finite \(p\)-groups of exponent \(p^e\) all of whose cyclic subgroups of order \(p^e\) are normal.

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Finite \(p\)-groups with some isolated subgroups

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On a question of G. Glauberman about a replacement theorem for finite \(p\)-groups

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Über den Frobenius'schen Klassenbegriff in nilpotenten Gruppen

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Über den Frobeniusschen Klassenbegriff in nilpotenten Gruppen. II

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Über die Anzahl der eigentlichen Untergruppen und der Elemente von gegebener Ordnung in \(p\)-Gruppen

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A class of descendant \(p\)-groups of order \(p^{9}\) and Higman's PORC conjecture

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Space groups and groups of prime-power order. I

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The Breadth and the Class of a Finite <i>P</i> -Group

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Outer Automorphisms in Nilpotent <i>p</i> -Groups of Class 2

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Minimal classes and maximal class in \(p\)-groups

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2-subnormal quadratic offenders and Oliver's <i>p</i>-group conjecture

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The breadth of finite <i>p</i>-groups, I

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Groups of breadth four have class five

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Some p-groups of Frobenius and extra-special type

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Elements of minimal breadth in finite <i>p</i>-groups and lie algebras

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The derived length of \(p\)-groups

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Spreads and nilpotence class in nilpotent groups and Lie algebras.

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Unstable homotopy classification of

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On coclass and trivial Schur multiplicator.

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The \(p\)-group generation algorithm

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Equivalences of classifying spaces completed at odd primes

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Equivalences of classifying spaces completed at the prime two

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\(p\)-groups of small breadth

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Finite \(p\)-groups in which the number of subgroups of possible order is less than or equal to \(p^3\).

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Non-inner automorphisms of order \(p\) in finite \(p\)-groups of coclass 3

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The Existence of Outer Automorphisms of Some Nilpotent Groups of Class 2

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Normal \(p\)-subgroups in the group of outer automorphisms of a finite \(p\)-group.

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A cohomological property of regular \(p\)-groups

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On a conjecture about automorphisms of finite \(p\)-groups.

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The structure of finite \(p\)-groups: Effective proof of the coclass conjectures

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Breadth and commutator subgroups of p-groups

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Groups of order $p^8$ and exponent $p$

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Non-PORC behaviour in groups of order \(p^{7}\)

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Groups with boundedly finite classes of conjugate elements

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2-groups of breadth 3.

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The power structure of finite p-groups

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A note on Oliver's \(p\)-group conjecture

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Finite groups and fusion systems

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On Hua-Tuan's conjecture.

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On Hua-Tuan's conjecture. II.

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1007/S11464-022-1001-6

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Sitelinks

Mathematics(1 entry)

mardi Publication:2080925

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