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Page 25 of Mathematical Reviews Vol. , Issue 2004a
[page]

2004
*
Mathematical Reviews
*

Let G be

*a**finite*p-*group*(p*a*prime)*of*exponent p and*nilpotent*class 4, and consider*a*3-step*Fibonacci**sequence*r = (r;)*in*G, with some initial data ro, r; and rz. ...*a**finite**nilpotent**group*. ...##
###
Page 3076 of Mathematical Reviews Vol. , Issue 99e
[page]

1999
*
Mathematical Reviews
*

Soc. (2) 49 (1994), no. 1, 83-92; MR 94k:20059] showed that the lengths

*of*ordinary 2-step*Fibonacci**sequences*are equal to the length*of*the 2-step*Fibonacci*recurrences*in**finite**nilpotent**groups**of*...*Fibonacci*Quart. 36 (1998), no. 3, 216-221. The study*of**Fibonacci**sequences**in**groups*began with work*of*D. D. Wall [Amer. Math. ...##
###
Page 4218 of Mathematical Reviews Vol. , Issue 82j
[page]

1982
*
Mathematical Reviews
*

*In*Section 3 there is

*a*gap

*in*the discussion

*of*equations over cyclic

*groups*. The example given there illustrates

*a*new

*application*

*of*small cancellation theory. ... He proves (Theorem 1) that they are then

*finite*extensions

*of*

*a*subgroup B whose centre is

*of*

*finite*index, such that for every element

*in*the

*group*but not

*in*B the centralizer

*in*the whole

*group*is

*finite*...

##
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Page 5903 of Mathematical Reviews Vol. , Issue 96j
[page]

1996
*
Mathematical Reviews
*

Any noncyclic relatively free

*group**of**finite*rank*in**a*variety ... They use the famous Tits theorem*in*proving that*a*relatively free*group*that is not*nilpotent*-by-abelian-by-*finite*has automorphism*group*that is not linear over*a*field*of*characteristic zero. ...##
###
Page 2726 of Mathematical Reviews Vol. , Issue 96e
[page]

1996
*
Mathematical Reviews
*

The author defines

*a**sequence**of**groups*(k) "ae ee F,*) = (a1,°++,@n| @i@j,) =@i42, 1=1,2,---,m) which are generalisations*of*the*Fibonacci**groups*(the case k = 1). ... It follows as*a*corollary that G is*finite*-by-*nilpotent*if and only if the Frattini factor*group*G/®(G) is*finite*-by-*nilpotent*. H. ...##
###
Infinite systems of linear equations and mathematical logic

2002
*
Linear Algebra and its Applications
*

We will demonstrate

doi:10.1016/s0024-3795(01)00537-7
fatcat:2rfdc64l3fgjhmkdm62ub7kd6e
*a*result*in*linear algebra which is*a*consequence*of**a*now classical result*of*mathematical logic, and then illustrate an*application**of*this result to*group*theory. ... It was demonstrated*in*[1] that the fundamental period*of**a**Fibonacci**sequence**in**a**finite*p-*group**of*exponent p > 3 and*nilpotency*class at most 4 is*a*divisor*of*the fundamental period*of*the usual ...*Fibonacci**sequence**in*the integers modulo p. ...##
###
Page 6566 of Mathematical Reviews Vol. , Issue 2003i
[page]

2003
*
Mathematical Reviews
*

*In*this paper the main result is the following. Theorem: Let G be

*a*nontrivial

*finite*p-

*group*

*of*exponent p and

*nilpotency*class 2. Then we have k(G) =k. ... 2003i: 1 1025 2003i:11025 11B39 20D15 Dikici, Ramazan (TR-ATAED-MD; Erzurum); Ozkan, Engin (TR-ATAS; Erzurum) An

*application*

*of*

*Fibonacci*

*sequences*

*in*

*groups*. (English summary) Appl. Math. ...

##
###
Asymptotically optimal k-step nilpotency of quadratic algebras and the Fibonacci numbers
[article]

2016
*
arXiv
*
pre-print

It follows from the Golod--Shafarevich theorem that if R is an associative algebra given by n generators and d<n^2/4cos^-2(π/k+1) quadratic relations, then R is not k-step

arXiv:1601.00554v1
fatcat:a37ska755ne2rovg7mh5easnpq
*nilpotent*. ... We show that the above estimate is asymptotically optimal, and establish number*of*related results. For example, we show that for any k this estimate is attained for ifinitely many n. ... Acknowledgements We are grateful to the Max-Planck-Institute for Mathematics*in*Bonn and to IHES, where parts*of*this research have been done, for hospitality, support, and excellent research atmosphere ...##
###
Page 5798 of Mathematical Reviews Vol. , Issue 2001H
[page]

2001
*
Mathematical Reviews
*

| n=1,2,3,---} and

*Fibonacci**sequences*can be generated*in*real time by cellular automata with 1-bit inter-cell communications. ... It is shown that an algebra (*A*,z) is*nilpotent*iff it is*a*ho- momorphic image*of**a*subalgebra*of**a*quasi-cascade-product*of*unary*nilpotent*algebras; (*A*, ) is definite iff it is*a*homomorphic image*of*...##
###
Relatively Free Semigroups of Intermediate Growth

2001
*
Journal of Algebra
*

He proved that every f.g.

doi:10.1006/jabr.2000.8503
fatcat:5l2omizwljdpvm2qqnf6tokhzy
*group**of*polynomial growth contains*a**nilpotent*subgroup*of*w x*finite*index. ... Sapir proved w x 23 that the variety*of*all*nilpotent**groups**of*class c cannot be defined by the system*of*identities over*a**finite*set*of*variables even*in*the class*of*monoids for c G 2. ... The equality 160 shows that induces*a*one-to-one correspondence*Ä*4 between the set*of*all*finite**sequences*␣ as above and the set*of*all n words*of*the type ⌬ U over the alphabet ⌽. ...##
###
On the Basick-nacci Sequences in Finite Groups

2011
*
Discrete Dynamics in Nature and Society
*

We define the basick-nacci

doi:10.1155/2011/639476
fatcat:jsgg5c3lizfire4r547c73eyd4
*sequences*and the basic periods*of*these*sequences**in**finite**groups*, then we obtain the basic periods*of*the basick-nacci*sequences*and the periods*of*thek-nacci*sequences**in*... symmetric groupS4, its subgroups, and binary polyhedral*groups*which related with these*groups*. ... Acknowledgments The authors thank the referees for their valuable suggestions which improved the presentation*of*the paper. ...##
###
Page 2659 of Mathematical Reviews Vol. , Issue 93e
[page]

1993
*
Mathematical Reviews
*

*In*Section 2, it is shown that an elementary nilpo- tent Lie

*group*can act freely and distally on some nilmanifold.

*A*nilmanifold is

*a*quotient

*of*

*a*

*nilpotent*Lie

*group*by

*a*uniform lattice. ... Contents: Alejandro Adem, On the geometry and cohomology

*of*

*finite*simple

*groups*(1-9); D. J. Benson [David John Benson], Resolutions and Poincaré duality for

*finite*

*groups*(10-19);

*A*. J. ...

##
###
The Metallic Ratio of Pulsating Fibonacci Sequences

2022
*
Symmetry
*

*In*this paper, we investigate the metallic ratio—

*a*generalized version

*of*the golden ratio—

*of*pulsating

*Fibonacci*

*sequences*

*in*three forms. ... The third form is the

*Fibonacci*

*sequence*

*in*bipolar quantum linear algebra (BQLA), which also pulsates. ... We would like to express our appreciation to Rasimate Maungchang for triggering the golden ratio issue during our research on the pulsating pm, cq-

*Fibonacci*

*sequence*. ...

##
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Page 3818 of Mathematical Reviews Vol. , Issue 95g
[page]

1995
*
Mathematical Reviews
*

Abbott (3-AB; Edmonton, AB)
95g:11009 11B39 20D15 Aydin, Huseyin (TR-ATAS; Erzurum); Smith, Geoff C. (4-BATH-SM; Bath) Fourier analysis

*in**finite**nilpotent**groups*. ...*Applications**of**Fibonacci*numbers, Vol. 5 (St. Andrews, 1992), 49-59, Kluwer Acad. Publ., Dordrecht, 1993. Let s = (s;), so =0, s; = 1, denote the ordinary*Fibonacci*se- quence, modulo n. ...##
###
Page 6213 of Mathematical Reviews Vol. , Issue 94k
[page]

1994
*
Mathematical Reviews
*

Smith, Fourier analysis

*in**finite**nilpotent**groups*(49-59); Huseyin Aydin, Ramazan Dikici and Geoff C. ... Peter Gumm (D-MRBG; Marburg) See also 20070. 11 NUMBER THEORY 94k:11001 11-06 11B39 ¥**Applications**of**Fibonacci*numbers. Vol. 5. ...
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