Equation 677 Database

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Magma 692c1e7c18cc…

magma 692c1e7c18cc
Size
705
Isomorphism class hash
692c1e7c18cc6c0a5bbc84df3e5a6a180ad3c8e35d344bd0ea2956cb499d3164
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 21:19:04
Display reorder
660,468,466,245,463,470,432,243,431,425,422,450,448,244,444,452,523,241,530,528,532,242,490,488,483,492,240,510,508,503,512,251,588,590,583,592,249,548,550,543,552,250,568,570,563,572,648,247,650,643,652,608,248,610,603,612,628,246,630,623,632,691,689,697,699,471,467,11,465,469,426,9,421,424,423,453,449,10,446,451,525,7,533,529,531,8,493,489,485,491,6,513,509,505,511,2,589,593,585,591,1,549,553,545,551,0,569,573,565,571,649,5,653,645,651,609,3,613,605,611,629,4,633,625,631,685,690,692,687,72,338,113,89,63,73,111,87,64,336,74,337,112,88,65,85,109,75,341,62,110,76,339,86,60,108,77,340,84,61,119,344,78,95,69,117,342,79,93,70,118,343,80,94,71,347,115,81,91,68,345,116,82,92,66,346,114,83,90,67,681,664,680,670,288,322,163,305,148,289,164,303,149,323,290,321,162,304,147,301,166,291,318,144,167,292,319,302,145,165,293,320,300,146,161,313,294,311,154,159,314,295,309,155,160,312,296,310,153,316,157,297,307,150,317,158,298,308,151,315,156,299,306,152,677,683,662,666,474,473,121,461,460,434,122,429,428,433,458,457,120,442,440,520,124,538,537,521,125,498,497,481,480,123,518,517,501,500,127,597,598,580,581,128,557,558,541,540,126,577,578,560,561,657,130,658,640,641,617,131,618,601,600,637,129,638,621,620,695,700,702,703,477,476,253,478,479,436,254,438,439,437,441,447,252,454,456,534,256,527,526,536,257,487,486,494,496,255,507,506,514,516,259,586,587,594,596,260,546,547,554,556,258,566,567,574,576,646,262,647,654,656,606,263,607,614,616,626,261,627,634,636,688,686,698,694,472,475,232,464,462,427,233,420,430,435,455,459,231,445,443,524,228,535,539,522,229,495,499,484,482,230,515,519,504,502,238,599,595,584,582,239,559,555,544,542,237,579,575,564,562,659,234,655,644,642,619,235,615,604,602,639,236,635,624,622,696,693,704,701,15,350,26,374,386,16,24,372,384,348,17,349,25,373,385,377,29,14,353,389,27,12,351,375,387,28,13,352,376,388,32,356,21,380,392,30,354,22,378,390,31,355,23,379,391,359,35,20,383,395,357,33,18,381,393,358,34,19,382,394,682,665,675,674,49,171,37,410,180,50,38,408,181,172,48,173,36,409,182,413,40,52,170,183,41,53,168,411,184,39,51,169,412,185,43,177,55,416,186,44,178,56,414,187,42,179,54,415,188,176,46,58,419,189,174,47,59,417,190,175,45,57,418,191,669,679,667,684,265,398,96,276,326,266,97,277,324,396,264,397,98,278,325,279,99,268,401,329,100,269,399,280,327,101,267,400,281,328,102,404,271,282,332,103,402,272,283,330,104,403,270,284,331,407,105,274,285,335,405,106,275,286,333,406,107,273,287,334,663,678,661,671,209,362,141,227,192,207,142,225,193,360,208,361,143,226,194,223,140,205,365,195,138,206,363,224,196,139,204,364,222,197,132,368,215,218,198,133,366,213,216,199,134,367,214,217,200,371,135,211,221,201,369,136,212,219,202,370,137,210,220,203,668,672,676,673 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#e6ff3ea71fab369083c7c0ebcc1e5818a214c988729d733a41fa2a4b44566c90, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 21:19:05 · history