Equation 677 Database

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Magma ab6088f9c3ed…

magma ab6088f9c3ed
Size
705
Isomorphism class hash
ab6088f9c3ed99c2567f8a208b1b35d03614b968f3d0c5704b3ebed2f73aa348
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 21:53:28
Display reorder
660,512,505,506,63,504,532,64,525,526,524,485,62,492,486,484,432,425,59,426,424,451,449,60,450,448,472,465,61,466,464,625,626,632,69,624,645,646,652,70,644,605,606,612,68,604,546,545,552,65,544,566,565,572,66,564,586,585,592,67,584,687,686,695,688,516,500,509,125,507,536,126,520,529,527,480,127,496,489,487,436,421,128,429,427,459,454,129,458,443,476,460,130,469,467,621,629,636,123,627,640,649,656,124,647,601,609,616,122,607,549,540,558,119,547,569,560,578,120,567,589,581,598,121,587,692,690,702,689,279,350,398,145,410,280,143,351,399,411,349,144,278,397,409,275,346,148,394,406,276,347,146,395,407,277,348,147,396,408,356,404,285,151,416,357,405,286,149,417,355,403,284,150,415,400,352,281,154,412,401,353,282,152,413,402,354,283,153,414,672,680,661,679,167,196,264,97,182,168,95,194,265,183,195,96,169,263,184,170,192,100,267,181,171,193,98,268,179,172,191,99,266,180,202,270,173,103,188,200,271,174,101,189,201,269,175,102,190,273,198,176,106,187,274,199,177,104,185,272,197,178,105,186,667,663,662,670,508,513,511,131,510,528,132,533,531,530,493,133,488,491,490,428,433,134,431,430,444,447,135,446,445,468,473,136,471,470,633,631,628,137,630,653,651,648,138,650,613,611,608,139,610,551,555,548,140,550,571,575,568,141,570,591,595,588,142,590,698,696,701,693,518,519,517,80,514,538,81,539,537,534,499,82,498,497,494,438,439,79,437,434,441,442,77,440,452,477,479,78,478,474,639,638,637,71,634,657,658,659,72,654,619,618,617,73,614,553,559,554,74,556,573,579,574,75,576,593,599,594,76,596,704,700,697,699,502,503,501,51,515,522,52,523,521,535,483,50,482,481,495,422,423,47,420,435,456,457,48,455,453,462,463,49,461,475,623,620,622,57,635,643,641,642,58,655,603,600,602,56,615,541,543,542,53,557,561,563,562,54,577,580,583,582,55,597,703,694,685,691,14,233,367,258,29,12,259,234,369,30,235,257,13,365,31,17,236,261,359,32,15,237,262,361,33,16,238,260,363,34,231,378,20,256,24,232,380,18,254,419,230,376,19,255,25,370,227,23,252,26,372,228,21,253,27,374,229,22,251,28,683,681,675,674,326,314,41,115,84,327,113,315,42,85,313,114,325,43,83,322,310,118,44,87,323,311,116,45,88,324,312,117,46,86,320,39,332,110,90,321,40,333,111,91,319,38,331,112,89,35,316,328,109,93,36,317,329,107,94,37,318,330,108,92,664,676,668,684,386,209,338,166,1,387,164,210,339,0,211,165,385,337,2,382,212,162,334,3,383,213,163,335,4,384,214,161,336,5,207,344,392,157,6,208,345,393,155,7,206,343,391,156,8,340,203,388,160,9,341,204,389,158,10,342,205,390,159,11,678,665,677,669,294,366,248,216,299,292,217,368,249,300,364,215,293,250,298,297,358,219,247,302,295,360,220,245,303,296,362,218,246,301,379,239,287,222,305,381,240,418,223,306,377,241,291,221,304,242,371,288,225,308,243,373,289,226,309,244,375,290,224,307,673,671,682,666 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#fb895e2582be84c8b2721db1499636a6dec5ebe66e3b80b47964e64d8130d57b, 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 21:53:29 · history