عنوان

تاثیر درجات کاراکتر زیر گروه پی-مانده یک گروه بر روی ساختار آن,‮‭The influence of character degrees of -residual subgroup of a group on the structure of group‬

Number

‭۲۳۸۷۰پ‬

.Language of Text, Soundtrack etc

per

Title Proper

تاثیر درجات کاراکتر زیر گروه پی-مانده یک گروه بر روی ساختار آن

Parallel Title Proper

‮‭The influence of character degrees of -residual subgroup of a group on the structure of group‬

First Statement of Responsibility

/آمینه محمدزاده

Name of Publisher, Distributor, etc.

: علوم ریاضی

Date of Publication, Distribution, etc.

، ‮‭۱۳۹۹‬

Name of Manufacturer

، راشدی

Specific Material Designation and Extent of Item

‮‭۱۱۱‬ص‬

Text of Note

چاپی - الکترونیکی

Dissertation or thesis details and type of degree

دکتری

Discipline of degree

ریاضی محض گرایش جبر

Date of degree

‮‭۱۳۹۹/۰۶/۲۰‬

Body granting the degree

تبریز

Text of Note

B is the direct product of two normal subgroups, where cd(A) = 1, p and cd(B) = 1, m1, . . . , mk, m, n. Also, we determine the five-vertex character degree graph of nonsolvable groups. The prime character degree graph (G) of a finite group G is the graph whose vertices are all prime divisors of the degrees of the complex irreducible characters of G, with distinct primes p and q joined by an edge if pq divides (1) for some complex irreducible character of G. Lewis and White determined all graphs with at most four vertices that occur as (G) for some nonsolvable group G. In this thesis, we determine all graphs with five vertices- up to two exceptions that occuras (G) for some nonsolvable group G. Along with previously known results on prime character degree graphs of solvable groups, this completes the classification of all five-vertex graphs- up to two exceptions that occur as (G) for some finite group G ‌ mk, m, n, where m and n are relatively prime integers and m1, . . . , mk are all nontrivial and proper divisors of m, then under some conditions on p, m, and n, the group G = A , ╖ ╖ ╖ B is the direct product of two normal subgroups, where cd(A) = 1, p and cd(B) = 1, m, n or there is a prime t such that G has a normal Sylow tsubgroup and at least one of the m or n is a t-power, the power of t is greater than 1 and the Fitting height of G is at most 3. In this thesis, we extend this result and we prove that if G is a solvable group with cd(Op(G)) = 1, m1, ‌ Let G be a finite group and cd(G) be the set of all irreducible complex characters of G. Aziziheris proved that if cd(Op(G)) = 1, m, n cd(G), where m and n are relatively prime integers greater than 1, p is prime not dividing mn, and (p, m), (p, n) are strongly coprime pairs, then either there are normal subgroups A and B of G such that G = A

Parallel Title

‮‭The influence of character degrees of -residual subgroup of a group on the structure of group‬

محمدزاده، آمینه

Mohammadzadeh, Amineh

Public note

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