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Sylow is an English word starting with the letter S. With 10+ example sentences you'll see exactly how it works in context.

Rare word

Sylow in a sentence

Using Sylow

  • In the example corpus, sylow often appears in combinations such as: the sylow, sylow p-subgroup, sylow p-subgroups.

Context around Sylow

  • Average sentence length in these examples: 29.5 words
  • Position in the sentence: 2 start, 7 middle, 3 end
  • Sentence types: 12 statements, 0 questions, 0 exclamations

Often before:

longer 1×

Often after:

subgroups 2× group 1× theorems 1×

Sentence patterns with Sylow

These short patterns come directly from the example sentences and show how the word is often embedded:

applications since sylow s theorem 1× called a sylow p subgroup 1× define a sylow p subgroup 1× first the sylow p subgroups 1× groups the sylow subgroups of 1× has the sylow p subgroups 1× in a sylow p subgroup 1× no longer sylow subgroups and 1×

Sentence openings and endings

Common sentence openings:

as subgroups for 1× by contrast if 1× example applications since 1× in fact it 1× in order to 1× it has order 1×

Common sentence endings:

sylow p subgroup 2× and various others 1× by p cycles 1× family of examples 1× in the conjugation 1× in the group 1×

Words around Sylow

Just before it in the word index:

sylmar 27 syllogistic 12 syllogisms 14 syllogism 24 sylliboy 2 syllabuses 9

Just after it in the word index:

sylphide 2 sylt 2 sylva 54 sylvain 30 sylvamo 3 sylvan 42

Similar in corpus frequency:

aanand 16 abcd 16 abdurrahman 16 aberdour 16 abergele 16 abg 16

Corpus analysis for Sylow

  • In this selection, "sylow" usually appears in the middle of the sentence. The average example has 29.5 words, and this corpus slice is mostly made up of statements.
  • Around the word, longer, subgroups, group and theorems stand out and add context to how "sylow" is used.
  • Recognizable usage signals include applications since sylow s theorem and called a sylow p subgroup. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "sylow" sits close to words such as aanand, abcd and abdurrahman, which helps place it inside the broader word index.

Example types with sylow

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

One proof of the Sylow theorems exploits the notion of group action in various creative ways. (16 words)

Unitriangular matrix groups The Sylow subgroups of general linear groups are another fundamental family of examples. (16 words)

In order to prevent useless ambiguous forms from generating, build up the 2-Sylow group Sll 2 (Δ) of G(Δ). (21 words)

Longer example sentences

By contrast, if n is even, then 4 divides the order of the group, and the subgroups of order 2 are no longer Sylow subgroups, and in fact they fall into two conjugacy classes, geometrically according to whether they pass through two vertices or two faces. (46 words)

It has order 60, and has 24 cyclic permutations of order 5, and 20 of order 3. Wilson's theorem Part of Wilson's theorem states that : for every prime p. One may easily prove this theorem by Sylow's third theorem. (42 words)

We define a Sylow p-subgroup in an infinite group to be a p-subgroup (that is, every element in it has p-power order) that is maximal for inclusion among all p-subgroups in the group. (37 words)

Example sentences (12)

As subgroups, for a given prime p one has the Sylow p-subgroups P (largest p-subgroup not unique but all conjugate) and the p-core (the unique largest normal p-subgroup), and various others.

By contrast, if n is even, then 4 divides the order of the group, and the subgroups of order 2 are no longer Sylow subgroups, and in fact they fall into two conjugacy classes, geometrically according to whether they pass through two vertices or two faces.

Example applications Since Sylow's theorem ensures the existence of p-subgroups of a finite group, its worthwhile to study groups of prime power order more closely.

In fact, it contains a p-group of maximal possible order: if where p does not divide m, then G has a subgroup P of order called a Sylow p-subgroup.

In order to prevent useless ambiguous forms from generating, build up the 2-Sylow group Sll 2 (Δ) of G(Δ).

It has order 60, and has 24 cyclic permutations of order 5, and 20 of order 3. Wilson's theorem Part of Wilson's theorem states that : for every prime p. One may easily prove this theorem by Sylow's third theorem.

One proof of the Sylow theorems exploits the notion of group action in various creative ways.

These rely on J. L. Alperin 's strengthening of the conjugacy portion of Sylow's theorem to control what sorts of elements are used in the conjugation.

Advertentie

They are more easily described in special cases first: The Sylow p-subgroups of the symmetric group of degree p are just the cyclic subgroups generated by p-cycles.

This subgroup need not be unique, but any subgroups of this order are conjugate, and any p-subgroup of G is contained in a Sylow p-subgroup.

Unitriangular matrix groups The Sylow subgroups of general linear groups are another fundamental family of examples.

We define a Sylow p-subgroup in an infinite group to be a p-subgroup (that is, every element in it has p-power order) that is maximal for inclusion among all p-subgroups in the group.

Advertentie

Common combinations with sylow

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "sylow" in a sentence?
An example: "As subgroups, for a given prime p one has the Sylow p-subgroups P (largest p-subgroup not unique but all conjugate) and the p-core (the unique largest normal p-subgroup), and various others." This page contains 10+ example sentences with the word "sylow" from authentic English texts.
How many example sentences with "sylow" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "sylow", drawn from a database of millions of English sentences.