Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 6120f1093b44…

magma 6120f1093b44
Size
381
Isomorphism class hash
6120f1093b44048328946dc6e22695f58eb63f0110df3c38aa36f7f7508a8dac
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:38:38
Display reorder
380,236,246,241,261,250,255,159,164,169,144,149,154,44,49,38,29,34,299,215,205,210,230,221,226,319,320,318,322,323,321,279,267,272,292,282,285,109,99,104,94,84,89,6,14,5,8,201,7,184,174,179,199,189,194,79,69,74,64,54,59,119,114,124,129,134,139,336,344,354,368,364,379,349,334,355,370,235,245,240,260,251,256,155,160,165,141,146,151,40,46,35,25,30,296,216,206,211,231,220,225,305,303,304,302,301,300,276,265,270,291,280,286,106,96,102,92,82,86,10,11,9,13,200,12,181,171,176,196,185,190,77,66,71,60,50,55,115,110,120,126,131,135,335,341,350,369,362,376,345,331,356,371,238,248,243,263,253,258,156,161,166,140,145,150,41,47,36,26,31,295,218,208,213,233,223,228,327,328,329,324,325,326,277,268,273,293,283,287,105,95,100,90,80,85,21,24,20,23,203,22,180,170,175,195,186,191,76,67,72,62,52,57,116,111,121,125,130,136,338,340,351,365,361,375,346,330,358,373,239,249,244,264,254,259,157,162,167,142,147,152,42,45,39,27,32,297,219,209,214,234,224,229,313,314,312,316,317,315,278,269,274,294,284,288,107,97,101,91,81,87,3,4,2,0,204,1,182,172,177,197,187,192,75,65,70,61,51,56,117,112,122,127,132,137,339,342,353,366,360,377,347,332,359,374,237,247,242,262,252,257,158,163,168,143,148,153,43,48,37,28,33,298,217,207,212,232,222,227,311,309,310,308,306,307,275,266,271,290,281,289,108,98,103,93,83,88,16,17,15,19,202,18,183,173,178,198,188,193,78,68,73,63,53,58,118,113,123,128,133,138,337,343,352,367,363,378,348,333,357,372 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#a6a871b690da3ca50898b154241f95e49e76adc5851f18be5057763f1765447f, M = {67} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 51.

last edited by qawbecrdtey at 2026-10-01 23:38:39 · history