Some unsolvable conjectures in finite \(p\)-groups
type: Item
instance of: scholarly article
title: Some unsolvable conjectures in finite \(p\)-groups
zbMATH Open document ID: 1496.20034
author: Qinhai Zhang
published in: Frontiers of Mathematics in China
publication date: 2022-10-12T00:00:00Z
Mathematics Subject Classification ID: 20D15
zbMATH DE Number: 7599899
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: Hua-Tuan conjecture
zbMATH Keywords: Higman conjecture
zbMATH Keywords: Oliver conjecture
zbMATH Keywords: Wiegold conjecture
describes a project that uses: GAP
MaRDI profile type: Publication
full work available at URL: s11464-022-1001-6
OpenAlex ID: W4280604375
Wikidata QID: Q122984436
cites work: Finite \(p\)-groups of class 2 have noninner automorphisms of order \(p\).
cites work: Powerful \(p\)-groups have non-inner automorphisms of order \(p\) and some cohomology.
cites work: Finite \(p\)-groups of class 3 have noninner automorphisms of order \(p\).
cites work: On a Special Class of Regular p-Groups
cites work: Large Abelian Subgroups of p-Groups
cites work: Q3708174
cites work: SOME PROPERTIES OF SEMI-ABELIAN -GROUPS
cites work: On a nonregular \(p\)-group
cites work: On the Number of Subgroups of Given Order in a Finite p-Group of Exponent p
cites work: Groups of prime power order. Vol. 1.
cites work: Groups of prime power order. Vol. 2.
cites work: Groups of prime power order. Vol. 3.
cites work: Groups of prime power order. Vol. 5.
cites work: Groups of prime power order. Vol. 6.
cites work: On the existence of a noninner automorphism of order \(p\) for \(p\)-groups.
cites work: On the orders of automorphism groups of finite groups. II
cites work: Q3344124
cites work: Class and Breadth of a Finite p -Group
cites work: The nilpotency class of \(p\)-groups in which subgroups have few conjugates.
cites work: Noninner automorphisms of order \(p\) of finite \(p\)-groups
cites work: Non-PORC behaviour of a class of descendant \(p\)-groups.
cites work: Q5786051
cites work: Q5811242
cites work: The class-breadth conjecture revisited.
cites work: Higman's PORC conjecture for a family of groups
cites work: A Note on the Automorphism Group of a p-Group
cites work: Q3894108
cites work: Space Groups and Groups of Prime-Power Order IV. Counterexamples to the Class-Breadth Conjecture
cites work: Noninner automorphisms of order \(p\) in finite \(p\)-groups of coclass 2, when \(p>2\).
cites work: On the breadth of a finite p-group
cites work: Nichtabelsche p-Gruppen besitzen äußere p-Automorphismen
cites work: Groups of prime power order with many conjugacy classes
cites work: Large Abelian subgroups of finite \(p\)-groups
cites work: Abelian subgroups of small index in finite p-groups
cites work: Existence of normal subgroups in finite \(p\)-groups.
cites work: A partial analogue of Borel's fixed point theorem for finite \(p\)-groups.
cites work: \(p\)-groups with maximal elementary Abelian subgroups of rank 2.
cites work: FINITE -GROUPS WITH SMALL AUTOMORPHISM GROUP
cites work: On Oliver's \(p\)-group conjecture.
cites work: On Oliver's \(p\)-group conjecture. II.
cites work: On a strong form of Oliver's \(p\)-group conjecture.
cites work: Weak closure and Oliver's \(p\)-group conjecture.
cites work: Enumerating p -Groups. I: Inequalities
cites work: Enumerating p -Groups, II: Problems Whose Solution is PORC
cites work: Partial Difference Sets
cites work: ON THE EXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER TWO IN FINITE 2-GROUPS
cites work: Finite nonabelian \(2\)-groups all of whose minimal nonabelian subgroups are metacyclic and have exponent \(4\).
cites work: Finite \(p\)-groups with many minimal nonabelian subgroups.
cites work: Finite \(p\)-groups of exponent \(p^e\) all of whose cyclic subgroups of order \(p^e\) are normal.
cites work: Finite \(p\)-groups with some isolated subgroups
cites work: On a question of G. Glauberman about a replacement theorem for finite \(p\)-groups
cites work: Über den Frobenius'schen Klassenbegriff in nilpotenten Gruppen
cites work: Über den Frobeniusschen Klassenbegriff in nilpotenten Gruppen. II
cites work: Über die Anzahl der eigentlichen Untergruppen und der Elemente von gegebener Ordnung in \(p\)-Gruppen
cites work: A class of descendant \(p\)-groups of order \(p^{9}\) and Higman's PORC conjecture
cites work: Q4544915
cites work: Space groups and groups of prime-power order. I
cites work: The Breadth and the Class of a Finite P -Group
cites work: Outer Automorphisms in Nilpotent p -Groups of Class 2
cites work: Q4761403
cites work: Minimal classes and maximal class in \(p\)-groups

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: 2-subnormal quadratic offenders and Oliver's p-group conjecture

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: The breadth of finite p-groups, I

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Groups of breadth four have class five

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Some p-groups of Frobenius and extra-special type

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Q4946828

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Elements of minimal breadth in finite p-groups and lie algebras

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: The derived length of \(p\)-groups

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Spreads and nilpotence class in nilpotent groups and Lie algebras.

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Unstable homotopy classification of

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Q3378959

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Q4426043

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: On coclass and trivial Schur multiplicator.

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: The \(p\)-group generation algorithm

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Equivalences of classifying spaces completed at odd primes

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Equivalences of classifying spaces completed at the prime two

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: \(p\)-groups of small breadth

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Finite \(p\)-groups in which the number of subgroups of possible order is less than or equal to \(p^3\).

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Non-inner automorphisms of order \(p\) in finite \(p\)-groups of coclass 3

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: The Existence of Outer Automorphisms of Some Nilpotent Groups of Class 2

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Normal \(p\)-subgroups in the group of outer automorphisms of a finite \(p\)-group.

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: A cohomological property of regular \(p\)-groups

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: On a conjecture about automorphisms of finite \(p\)-groups.

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: The structure of finite \(p\)-groups: Effective proof of the coclass conjectures

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Q5798835

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Breadth and commutator subgroups of p-groups

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Groups of order $p^8$ and exponent $p$

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Non-PORC behaviour in groups of order \(p^{7}\)

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Groups with boundedly finite classes of conjugate elements

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: 2-groups of breadth 3.

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: The power structure of finite p-groups

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Q3786631

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: A note on Oliver's \(p\)-group conjecture

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: Finite groups and fusion systems

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: On Hua-Tuan's conjecture.

Some unsolvable conjectures in finite \(p\)-groups (cites work)
cites work: On Hua-Tuan's conjecture. II.

Some unsolvable conjectures in finite \(p\)-groups (DOI)
DOI: 10.1007/S11464-022-1001-6