On groups with a splitting automorphism of prime order

1992 ◽  
Vol 34 (2) ◽  
pp. 360-362
Author(s):  
E. I. Khukhro
Keyword(s):  
Prime Order ◽  
Splitting Automorphism

A solvable group admitting a regular splitting automorphism of prime order is nilpotent

1978 ◽  
Vol 17 (5) ◽  
pp. 402-406 ◽  
Author(s):  
E. I. Khukhro
Keyword(s):  
Solvable Group ◽  
Prime Order ◽  
Regular Splitting ◽  
Splitting Automorphism

Nilpotency of solvable groups admitting a splitting automorphism of prime order

1980 ◽  
Vol 19 (1) ◽  
pp. 77-84 ◽  
Author(s):  
E. I. Khukhro
Keyword(s):  
Prime Order ◽  
Solvable Groups ◽  
Splitting Automorphism

Functional encryption for computational hiding in prime order groups via pair encodings

2017 ◽  
Vol 86 (1) ◽  
pp. 97-120 ◽  
Author(s):  
Jongkil Kim ◽  
Willy Susilo ◽  
Fuchun Guo ◽  
Man Ho Au
Keyword(s):  
Prime Order ◽  
Functional Encryption

scholarly journals On the normalizers of elements of prime order in simple groups

1974 ◽  
Vol 29 (3) ◽  
pp. 387-400 ◽  
Author(s):  
J.A Cohn
Keyword(s):  
Prime Order ◽  
Simple Groups

scholarly journals The eta invariant and equivariant bordism of flat manifolds with cyclic holonomy group of odd prime order

2009 ◽  
Vol 37 (3) ◽  
pp. 275-306 ◽  
Author(s):  
Peter B. Gilkey ◽  
Roberto J. Miatello ◽  
Ricardo A. Podestá
Keyword(s):  
Prime Order ◽  
Holonomy Group ◽  
Eta Invariant ◽  
Flat Manifolds ◽  
Equivariant Bordism

Holonomy Groups of Prime Order

1986 ◽  
pp. 104-166
Author(s):  
Leonard S. Charlap
Keyword(s):  
Prime Order ◽  
Holonomy Groups

CCA-secure Predicate Encryption from Pair Encoding in Prime Order Groups: Generic and Efficient

2017 ◽  
pp. 85-106 ◽  
Author(s):  
Sanjit Chatterjee ◽  
Sayantan Mukherjee ◽  
Tapas Pandit
Keyword(s):  
Prime Order ◽  
Predicate Encryption

scholarly journals Atomic Latin Squares based on Cyclotomic Orthomorphisms

10.37236/1919 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Ian M. Wanless
Keyword(s):  
Finite Fields ◽  
Complete Graph ◽  
Prime Order ◽  
Automorphism Groups ◽  
Latin Square ◽  
Latin Squares ◽  
Established Method ◽  
Cyclic Groups ◽  
Complete Bipartite Graphs ◽  
First Time

Atomic latin squares have indivisible structure which mimics that of the cyclic groups of prime order. They are related to perfect $1$-factorisations of complete bipartite graphs. Only one example of an atomic latin square of a composite order (namely 27) was previously known. We show that this one example can be generated by an established method of constructing latin squares using cyclotomic orthomorphisms in finite fields. The same method is used in this paper to construct atomic latin squares of composite orders 25, 49, 121, 125, 289, 361, 625, 841, 1369, 1849, 2809, 4489, 24649 and 39601. It is also used to construct many new atomic latin squares of prime order and perfect $1$-factorisations of the complete graph $K_{q+1}$ for many prime powers $q$. As a result, existence of such a factorisation is shown for the first time for $q$ in $\big\{$529, 2809, 4489, 6889, 11449, 11881, 15625, 22201, 24389, 24649, 26569, 29929, 32041, 38809, 44521, 50653, 51529, 52441, 63001, 72361, 76729, 78125, 79507, 103823, 148877, 161051, 205379, 226981, 300763, 357911, 371293, 493039, 571787$\big\}$. We show that latin squares built by the 'orthomorphism method' have large automorphism groups and we discuss conditions under which different orthomorphisms produce isomorphic latin squares. We also introduce an invariant called the train of a latin square, which proves to be useful for distinguishing non-isomorphic examples.

scholarly journals Euler’s criterion for prime order in the PID case

2020 ◽  
Vol 192 (3) ◽  
pp. 259-265
Author(s):  
Jagmohan Tanti
Keyword(s):  
Prime Order
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