Finite metacyclic<i>1‐e</i>and<i>1‐a</i>groups

Peterson, Gary L.

doi:10.1080/00927879508825488

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Classification Of the Finite Non-abelian 2-generated 2-groups1

Introduction and Main Results1

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1999

2023

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Cited by 5 publications

(2 citation statements)

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“…Moreover, one may observe that the metacyclic group (3, 2, 1, 1, −) does not appear at all in B. W. King's classification, the reason being exactly the above mentioned condition, which must be therefore ignored. The same remark was made by G. L. Peterson [5].…”

Section: Classification Of the Finite Non-abelian 2-generated 2-groupssupporting

confidence: 57%

Finite equilibrated 2-generated 2-groups

Silberberg

2006

Acta Math Hung

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A group is called equilibrated if no subgroup H of G can be written as a product of two non-normal subgroups of H. Blackburn, Deaconescu and Mann [1] investigated the finite equilibrated groups, giving a complete description of the non-soluble ones. On the other hand, they showed that the property of a finite nilpotent group of being equilibrated depends solely on the structure of its 2-generated p-subgroups. Consequently, all the finite 2-generated equilibrated pgroups were classified for any odd prime p, but the case p = 2 remained unsolved. This special case will represent the subject of the present paper.

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Section: Classification Of the Finite Non-abelian 2-generated 2-groupssupporting

confidence: 57%

Finite equilibrated 2-generated 2-groups

Silberberg

2006

Acta Math Hung

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“…There are many papers regarding polynomial automorphisms. For example, we can cite [1,11,13,14,17,20]. Also it is worth mentioning an interesting result of [8] stating that in a non-abelian finite simple group G, every function f G → G is polynomial; it follows that Aut G = PAut G in such a group.…”

Section: Introduction and Main Resultsmentioning

confidence: 97%

Polynomial Automorphisms of Soluble Groups

Endimioni

2009

Communications in Algebra

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A polynomial automorphism of a group G is an automorphism of the formWhen G is polycyclic, we prove that the set PAut G of all polynomial automorphisms forms a polycyclic subgroup of the automorphism group Aut G . When G is soluble, PAut G is not necessarily a subgroup, but we show that the subgroup generated by PAut G is soluble. We also give the general form of an element of PAut G when G is a torsion-free non-abelian metabelian nilpotent group.

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Split Metacyclic p-Groups That Are A-E Groups

Peterson

1999

Results. Math.

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Finite metacyclic1‐eand1‐agroups

Cited by 5 publications

References 3 publications

Finite equilibrated 2-generated 2-groups

Finite equilibrated 2-generated 2-groups

Polynomial Automorphisms of Soluble Groups

Split Metacyclic p-Groups That Are A-E Groups

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