Equation 677 Database

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Magma 88c77abb479d…

magma 88c77abb479d
Size
705
Isomorphism class hash
88c77abb479d238e3468aeeb36fd13c03b0a4713536dc1211db9e4eb5de2cc8c
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 17:35:55
Display reorder
660,42,578,562,569,570,43,589,598,582,590,44,549,558,542,550,45,638,622,629,630,46,658,642,649,650,47,618,602,609,610,40,538,522,529,530,41,498,482,489,490,39,518,502,509,510,449,36,440,445,446,476,37,461,468,469,436,38,420,428,429,699,695,687,685,158,565,567,572,568,156,592,585,587,588,157,552,545,547,548,161,625,627,632,628,159,645,647,652,648,160,605,607,612,608,164,525,527,532,528,162,485,487,492,488,163,505,507,512,508,451,167,452,447,444,464,165,466,471,467,424,166,426,431,427,702,692,690,689,93,223,188,201,379,94,202,224,186,380,95,203,222,187,378,92,226,191,200,382,90,227,189,198,383,91,225,190,199,381,84,221,183,192,377,85,219,184,193,375,86,220,185,194,376,217,87,182,195,373,218,88,180,196,374,216,89,181,197,372,661,677,674,680,125,11,31,403,355,123,404,9,32,356,124,402,10,30,354,121,7,34,406,358,122,8,35,407,359,120,6,33,405,357,131,2,29,401,353,129,1,27,399,351,130,0,28,400,352,5,127,25,397,349,3,128,26,398,350,4,126,24,396,348,667,681,670,676,169,564,566,574,577,170,594,584,586,597,168,554,544,546,557,172,624,626,634,637,173,644,646,654,657,171,604,606,614,617,175,524,526,534,537,176,484,486,494,497,174,504,506,514,517,442,178,443,454,456,463,179,465,472,475,423,177,425,432,435,704,686,697,700,61,561,579,575,571,62,595,581,599,591,60,555,540,559,551,64,621,639,635,631,65,641,659,655,651,63,600,619,615,611,67,521,539,535,531,68,480,499,495,491,66,501,519,515,511,450,70,457,455,453,460,71,477,473,470,421,69,437,433,430,698,701,688,703,15,573,563,576,560,16,596,593,583,580,17,556,553,543,541,14,633,623,636,620,12,653,643,656,640,13,613,603,616,601,21,533,523,536,520,22,493,483,496,481,23,513,503,516,500,458,20,459,448,441,479,18,478,474,462,438,19,439,434,422,693,694,691,696,147,236,282,295,209,148,296,234,283,207,149,294,235,284,208,146,239,285,298,205,144,237,286,299,206,145,238,287,297,204,153,231,280,293,215,154,232,281,291,213,155,233,279,292,214,230,152,276,289,211,228,150,277,290,212,229,151,278,288,210,682,669,673,664,309,73,58,319,391,310,320,74,59,392,311,318,72,57,390,308,76,54,322,394,306,77,55,323,395,307,75,56,321,393,300,79,49,317,389,301,80,50,315,387,302,78,48,316,388,82,303,52,313,385,83,304,53,314,386,81,305,51,312,384,684,672,675,665,138,100,260,109,367,139,110,101,258,368,140,108,99,259,366,141,96,263,112,370,142,97,261,113,371,143,98,262,111,369,136,106,255,115,365,137,107,256,116,363,135,105,257,114,364,102,132,254,118,361,103,133,252,119,362,104,134,253,117,360,662,683,671,678,246,331,415,343,271,247,344,332,416,272,248,342,330,414,270,249,334,418,346,274,250,335,419,347,275,251,333,417,345,273,244,329,413,341,269,245,327,411,339,267,243,328,412,340,268,325,240,409,337,265,326,241,410,338,266,324,242,408,336,264,666,679,663,668 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#5a6f57af4478d367dfac6487e89f811f842218c665866e576bd9224bcbc8a047, 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 17:35:59 · history