Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 1ccdc2fefea5…

magma 1ccdc2fefea5
Size
705
Isomorphism class hash
1ccdc2fefea5be1cf057a7271a4b3593b79e85d051d056f0603b92a7e07b0d08
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 17:40:45
Display reorder
660,20,587,550,575,554,18,585,551,573,552,19,549,574,553,586,583,23,546,571,557,584,21,547,572,555,582,22,548,570,556,578,541,15,566,560,576,542,16,564,558,577,540,17,565,559,544,581,14,569,563,545,579,12,567,561,543,580,13,568,562,687,688,686,685,175,224,349,220,198,176,222,350,221,199,174,348,219,200,223,227,178,352,216,201,225,179,353,217,202,226,177,351,218,203,230,347,173,211,204,228,345,171,212,205,229,346,172,210,206,343,233,169,214,207,344,231,170,215,208,342,232,168,213,209,703,704,701,702,107,539,494,518,514,105,537,492,516,515,106,493,517,513,538,535,103,497,521,510,536,104,495,519,511,534,102,496,520,512,530,500,98,524,505,528,498,96,522,506,529,499,97,523,504,503,533,101,527,508,501,531,99,525,509,502,532,100,526,507,671,672,670,669,242,401,357,389,366,240,399,358,387,367,241,359,388,368,400,397,245,356,385,369,398,243,354,386,370,396,244,355,384,371,392,363,237,380,372,390,364,238,378,373,391,365,239,379,374,362,395,236,383,375,360,393,234,381,376,361,394,235,382,377,679,680,678,677,413,154,158,261,252,411,155,156,262,253,412,157,263,254,153,150,409,161,260,255,151,410,159,258,256,152,408,160,259,257,145,164,404,267,250,146,162,402,268,251,144,163,403,269,249,167,148,407,266,246,165,149,405,264,247,166,147,406,265,248,692,691,690,689,61,445,455,290,466,62,446,453,288,467,60,454,289,465,444,448,64,451,293,462,449,65,452,291,463,447,63,450,292,464,443,461,67,285,472,441,459,68,286,473,442,460,66,287,471,457,439,70,284,468,458,440,71,282,469,456,438,69,283,470,699,700,698,697,36,134,32,123,115,37,132,30,124,116,38,31,125,114,133,137,39,35,122,118,135,40,33,120,119,136,41,34,121,117,140,27,42,129,113,138,28,43,130,111,139,29,44,131,112,26,143,45,128,109,24,141,46,126,110,25,142,47,127,108,663,664,662,661,296,626,596,622,600,294,624,594,623,601,295,595,621,602,625,629,299,599,618,603,627,297,597,619,604,628,298,598,620,605,632,591,302,613,606,630,592,300,614,607,631,593,301,612,608,590,635,305,616,609,588,633,303,617,610,589,634,304,615,611,682,683,684,681,77,651,648,650,649,75,655,652,654,653,76,657,658,656,659,647,73,646,644,645,638,74,636,637,639,643,72,640,642,641,488,180,83,480,479,486,181,81,481,477,487,182,82,482,478,183,491,79,483,475,184,489,80,484,476,185,490,78,485,474,695,696,693,694,48,90,420,274,429,49,91,421,275,430,50,422,273,431,92,93,51,423,270,428,94,52,424,271,426,95,53,425,272,427,88,418,54,280,435,89,419,55,281,436,87,417,56,279,437,414,84,57,276,434,415,85,58,277,432,416,86,59,278,433,667,668,665,666,187,318,341,314,2,188,319,339,312,1,186,340,313,0,320,321,190,337,317,5,322,191,338,315,3,323,189,336,316,4,324,332,193,309,8,325,330,194,310,6,326,331,192,311,7,335,327,196,308,11,333,328,197,306,9,334,329,195,307,10,675,676,673,674 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#5e8db79a467cc4283015956475779111852195ee797ae26ed1a0610c426b851f, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 17:40:47 · history