Skip to main content

Sylow, Peter Ludvig Mejdell

SYLOW, PETER LUDVIG MEJDELL

(b. Christiania [now Oslo], Norway, 12 December 1832; d. Christiania, 7 September 1918)

mathematics.

Sylow was the son of a cavalry captain, Thomas Edvard Sylow, who later became a minister of the government. After graduation from the Christiania Cathedral School in 1850, he studied at the university, where in 1853 he won a mathematics prize contest. He took the high school teacher examination in 1856, and from 1858 to 1898 he taught in the town of Frederikshald (now Halden). Sylow was awarded a scholarship to travel abroad in 1861, and he visited Berlin and Paris. In 1862–1863 he substituted for Ole-Jacob Broch at Christiania University; but until 1898 his only chance for a university chair came in 1869, and he was not appointed. Finally, through Sophus Lie, a special chair was created for him at Christiania University in 1898.

From 1873 to 1881 Sylow and Sophus Lie prepared a new edition of the works of N. H. Abel, and for the first four years Sylow was on leave from his school in order to devote himself to the project. In 1902, with Elling Holst, he published Abel’s correspondence. He also published a few papers on elliptic functions, particularly on complex multiplication, and on group theory.

Sylow’s name is best-known in connection with certain theorems in group theory and certain subgroups of a given group. In 1845 Cauchy had proved that any finite group G has subgroups of any prime order dividing the order of G. In 1872 Sylow published a 10-page paper containing the first extension of Cauchy’s result and perhaps the first profound discovery in abstract group theory after Cauchy. Sylow’s main theorem read as follows: First, if pm is the maximal power of p dividing the order of G, then G has subgroups of order pi for all i with 0≤i≤m, and in particular subgroups H of order pm (called p-Sylow groups): and the index j of the normalizer of H is congruent 1 mod p. Second, the p-Sylow groups of G are conjugate with each other. Sylow’s theorems were, and still are, a source of discoveries in group theory and are fundamental to most structural research in finite groups.

BIBLIOGRAPHY

I. Original Works. Sylow’s works are listed in H. B. Kragemo, “Bibliographie der Schriften Ludvig Sylows,” in Norsk matematisk forenings skrifter, 2nd ser., no. 3 (1933), 25–29. They include “ThÉorèmes sur les groupes de substitutions,” in Mathematische Annalen, 5 (1872), 584–594; and “Sur la multiplication complexe des fonctions elliptiques,” in Journal de mathÉmatiques pures et appliquÉes, 4th ser., 3 (1887), 109–254.

Sylow’s MSS are in the Oslo University Library, U.B. MS, fols. 730–808, and U.B. Brevsamling 7–8.

II. Secondary Literature. See T. Skolem, “Ludvig Sylow und seine wissenschaftlichen Arbeiten,” in Norsk matematisk forenings skrifter, 2nd ser., no. 2 (1933), 14–24: and C. Størmer, “Gedächtnisrede auf Professor Dr. P. L. M. Sylow,” ibid., no. 1 (1933), 7–13.

Hans Freudenthal

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"Sylow, Peter Ludvig Mejdell." Complete Dictionary of Scientific Biography. . Encyclopedia.com. 23 Oct. 2018 <https://www.encyclopedia.com>.

"Sylow, Peter Ludvig Mejdell." Complete Dictionary of Scientific Biography. . Encyclopedia.com. (October 23, 2018). https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/sylow-peter-ludvig-mejdell

"Sylow, Peter Ludvig Mejdell." Complete Dictionary of Scientific Biography. . Retrieved October 23, 2018 from Encyclopedia.com: https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/sylow-peter-ludvig-mejdell

Learn more about citation styles

Citation styles

Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

Notes:
  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.