Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma cf80a71770b7…

magma cf80a71770b7
Size
705
Isomorphism class hash
cf80a71770b71da9a9cf6f18293adf2ab3b5aeeb969e58a8ae671e4e6083fa51
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 16:38:44
Display reorder
660,255,58,575,583,594,592,59,253,576,584,60,593,254,574,585,597,251,61,578,582,252,595,62,579,580,596,250,63,577,581,600,246,56,573,589,598,244,57,571,590,572,599,245,55,591,249,603,52,569,588,247,601,53,570,586,248,602,54,568,587,687,688,686,685,129,362,327,328,350,351,363,127,325,329,361,349,128,326,330,346,125,358,323,331,126,347,359,324,332,348,124,360,322,333,341,135,353,318,334,342,133,354,316,335,317,340,134,352,336,131,344,356,321,337,132,345,357,319,338,130,343,355,320,339,703,704,701,702,243,566,531,534,545,546,567,241,529,532,565,544,242,530,533,548,239,562,527,537,240,549,563,528,535,547,238,564,526,536,551,234,557,522,540,552,232,558,520,538,521,550,233,556,539,237,554,560,525,543,235,555,561,523,541,236,553,559,524,542,671,672,670,669,7,151,18,370,145,146,152,8,16,371,153,147,9,17,372,144,6,150,21,373,4,142,148,19,374,143,5,149,20,375,136,13,157,24,368,137,14,158,22,369,23,138,15,159,367,12,139,156,27,364,10,140,154,25,365,11,141,155,26,366,679,680,678,677,167,410,423,376,398,399,411,168,421,377,409,397,166,422,378,394,170,406,419,379,171,395,407,420,380,396,169,408,418,381,389,165,401,414,382,390,163,402,412,383,413,388,164,400,384,161,392,404,417,385,162,393,405,415,386,160,391,403,416,387,692,691,690,689,187,495,496,462,473,474,493,188,497,460,494,472,189,498,461,476,186,491,499,465,184,477,492,500,463,475,185,490,501,464,479,193,486,502,468,480,194,484,503,466,504,478,195,485,467,192,482,489,505,471,190,483,487,506,469,191,481,488,507,470,699,700,698,697,74,85,91,100,121,122,86,75,92,101,87,123,73,93,102,120,70,84,90,103,71,118,82,88,104,119,72,83,89,105,112,65,76,97,106,113,66,77,98,107,99,114,64,78,108,68,115,79,96,109,69,116,80,94,110,67,117,81,95,111,663,664,662,661,260,614,627,630,642,640,615,261,625,628,613,641,259,626,629,645,256,610,623,633,257,643,611,624,631,644,258,612,622,632,648,266,605,618,636,646,267,606,616,634,617,647,265,604,635,262,651,608,621,639,263,649,609,619,637,264,650,607,620,638,682,683,684,681,513,1,221,224,202,203,0,511,219,225,2,204,512,220,223,205,509,3,218,222,510,652,653,654,655,656,508,657,658,659,200,519,206,214,226,201,517,207,212,227,213,199,518,208,228,515,196,209,217,229,516,197,210,215,230,514,198,211,216,231,695,696,693,694,183,439,448,32,432,430,440,181,449,33,441,431,182,450,31,435,179,438,451,28,180,433,436,452,29,434,178,437,453,30,427,174,445,454,38,428,172,446,455,39,456,429,173,447,37,177,426,444,457,34,175,424,442,458,35,176,425,443,459,36,667,668,665,666,40,315,270,281,302,303,313,41,268,282,314,301,42,269,280,298,43,311,273,284,44,299,312,271,285,300,45,310,272,283,293,46,306,276,287,294,47,304,274,288,275,292,48,305,286,49,296,309,279,290,50,297,307,277,291,51,295,308,278,289,675,676,673,674 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#3866b47acdf4717a31e27879d6448be53ada0b89c1671a7aec66e55c44000764, 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 16:38:45 · history