Equation 677 Database

← all  ·  ← by size  ·  ← size 684

Magma 97bc18e4fd75…

magma 97bc18e4fd75
Size
684
Isomorphism class hash
97bc18e4fd752ed4369624abee7b777a43187c859115c34bbdc143e2ea5ccbaa
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 683) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 13:46:49
Display reorder
681,679,680,675,676,677,682,678,683,302,303,308,309,310,311,312,313,305,306,307,299,300,301,293,294,295,296,297,298,304,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,314,620,619,621,622,623,624,625,626,627,628,629,615,616,617,618,75,76,81,82,83,84,85,86,78,79,80,72,73,74,66,67,68,69,70,71,77,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,108,109,110,111,112,113,114,115,116,117,118,119,1,0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,87,602,600,603,604,605,606,607,608,609,610,611,612,613,614,601,500,518,484,483,482,481,480,568,502,486,485,497,498,499,491,492,493,494,495,496,501,519,516,515,514,513,512,511,510,509,508,507,506,505,504,503,517,487,488,489,490,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,569,599,575,574,573,572,571,570,597,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,598,662,660,663,664,665,666,667,668,669,670,671,672,673,674,661,121,122,127,128,129,130,131,132,124,125,126,238,239,120,232,233,234,235,236,237,123,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,133,655,658,657,652,651,632,634,636,638,640,642,644,646,631,648,454,455,460,461,462,463,464,465,457,458,459,451,452,453,445,446,447,448,449,450,456,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,467,468,469,470,471,472,473,474,475,476,477,478,479,360,361,362,363,364,365,366,466,635,633,637,639,641,643,645,647,630,649,659,654,656,653,650 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 684 = 9 + 5*135, 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#d06be46a512d7443c089bc3030f3df281c845eba3c792e70152c014fa0d535cd, M = {135, 136, 137, 138, 139, 140, 141, 142, 143} 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, 135): MacNeish's product over GF(27) x GF(5); GF(27) = F_3[x]/(x^3 + 2x + 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: 1.

last edited by qawbecrdtey at 2026-10-08 13:46:50 · history