Equation 677 Database

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Magma 2f106322393c…

magma 2f106322393c
Size
705
Isomorphism class hash
2f106322393c44213a8c025e4d71563a68a84f6b1d742bd87865e59597be20c5
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 15:16:04
Display reorder
660,95,574,577,578,567,93,587,594,597,598,554,547,94,557,558,627,91,634,637,638,647,92,654,657,658,607,90,614,617,618,534,86,527,537,538,494,84,487,497,498,514,85,507,517,518,89,445,442,447,448,87,473,466,475,476,88,433,426,435,436,696,699,688,689,252,570,576,579,572,253,592,590,596,599,550,552,254,556,559,632,255,630,636,639,652,256,650,656,659,612,257,610,616,619,530,258,532,536,539,490,259,492,496,499,510,260,512,516,519,261,456,457,446,449,262,469,471,474,477,263,429,431,434,437,693,702,692,691,216,203,22,283,355,217,356,201,23,284,202,354,218,21,282,358,219,199,18,286,359,220,200,19,287,357,221,198,20,285,194,222,353,13,281,192,223,351,14,279,193,224,352,12,280,225,197,349,16,277,226,195,350,17,278,227,196,348,15,276,665,664,669,673,118,403,139,67,319,119,320,404,140,68,402,318,117,138,66,322,114,406,142,70,323,115,407,143,71,321,116,405,141,69,401,109,317,137,65,399,110,315,135,63,400,108,316,136,64,112,397,313,133,61,113,398,314,134,62,111,396,312,132,60,670,678,681,667,248,566,569,568,565,246,585,586,589,588,546,545,247,549,548,625,251,626,629,628,645,249,646,649,648,605,250,606,609,608,525,243,526,529,528,485,244,486,489,488,505,245,506,509,508,242,441,440,455,454,240,464,465,468,467,241,424,425,428,427,695,704,700,697,99,562,560,564,563,100,583,582,580,584,542,543,101,540,544,623,98,622,621,624,643,96,642,641,644,603,97,602,601,604,521,105,523,522,524,481,106,483,482,484,501,107,503,502,504,104,451,452,450,453,102,460,462,461,463,103,420,422,421,423,698,701,703,694,52,575,571,573,561,53,581,595,591,593,555,541,51,551,553,620,48,635,631,633,640,49,655,651,653,600,50,615,611,613,535,58,520,531,533,495,59,480,491,493,515,57,500,511,513,54,458,459,443,444,55,479,478,470,472,56,438,439,430,432,686,687,690,685,204,236,379,271,35,205,33,234,380,272,235,34,206,378,270,31,207,239,382,274,32,208,237,383,275,30,209,238,381,273,231,210,26,377,269,232,211,24,375,267,233,212,25,376,268,213,230,29,373,265,214,228,27,374,266,215,229,28,372,264,676,661,663,679,3,295,343,130,80,4,78,296,344,131,294,79,5,342,129,83,2,298,346,126,81,1,299,347,127,82,0,297,345,128,293,9,75,341,121,291,10,76,339,122,292,11,77,340,120,8,289,74,337,124,6,290,72,338,125,7,288,73,336,123,672,684,671,675,189,415,148,391,367,190,368,416,149,392,414,366,191,147,390,370,188,418,144,394,371,186,419,145,395,369,187,417,146,393,413,180,365,154,389,411,181,363,155,387,412,182,364,153,388,183,409,361,150,385,184,410,362,151,386,185,408,360,152,384,683,680,682,674,47,178,331,307,165,45,166,179,332,308,177,167,46,330,306,164,43,174,334,310,162,44,175,335,311,163,42,176,333,309,169,38,156,329,305,170,36,157,327,303,168,37,158,328,304,41,172,159,325,301,39,173,160,326,302,40,171,161,324,300,668,666,677,662 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#0f0ec421cc32f9c063215c008f5f1d2db6033828d1c93d9b7da541d2d3cf51f3, 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 15:16:06 · history