Equation 677 Database

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Magma f0ed956317df…

magma f0ed956317df
Size
705
Isomorphism class hash
f0ed956317df388d33c8b7b885e4e9b72faf82f81b468a04fb2c3523b7e7081e
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 15:16:35
Display reorder
660,133,491,196,297,210,134,211,492,194,298,490,209,135,195,296,206,136,494,199,300,207,137,495,197,301,208,138,493,198,299,489,139,216,202,295,487,140,217,200,293,488,141,215,201,294,142,485,212,205,291,143,486,213,203,292,144,484,214,204,290,678,674,680,686,347,418,150,455,169,348,167,419,151,456,417,168,349,149,454,165,346,421,146,458,166,344,422,147,459,164,345,420,148,457,416,338,160,156,453,414,339,158,157,451,415,340,159,155,452,341,412,163,152,449,342,413,161,153,450,343,411,162,154,448,667,665,663,672,305,25,405,178,515,306,516,26,406,176,27,514,307,404,177,518,304,28,408,181,519,302,29,409,179,517,303,30,407,180,31,311,513,403,173,32,312,511,401,174,33,313,512,402,175,310,34,509,399,172,308,35,510,400,170,309,36,508,398,171,676,673,685,683,11,621,626,625,622,12,630,628,634,633,613,614,10,618,617,646,7,645,650,649,654,8,652,658,657,638,9,637,642,641,604,2,606,610,609,588,3,590,594,593,596,0,598,602,601,5,572,574,577,576,6,581,582,586,585,4,61,132,532,435,702,699,704,703,270,229,381,235,393,271,394,227,382,233,228,392,269,380,234,396,266,225,384,231,397,267,226,385,232,395,268,224,383,230,220,276,391,379,241,218,277,389,377,239,219,275,390,378,240,272,223,387,375,237,273,221,388,376,238,274,222,386,374,236,690,689,693,691,16,503,540,443,80,17,81,504,541,444,502,82,18,539,442,83,15,506,543,446,84,13,507,544,447,85,14,505,542,445,501,22,78,538,441,499,23,79,536,439,500,24,77,537,440,21,497,74,534,437,19,498,75,535,438,20,496,76,533,436,669,664,668,661,332,479,122,113,90,333,91,480,123,114,478,89,334,121,112,86,335,482,125,110,87,336,483,571,570,88,337,481,124,111,477,330,96,128,116,475,331,97,126,117,476,329,95,127,115,326,473,92,131,119,327,474,93,129,120,328,472,94,130,118,695,696,692,694,102,430,527,48,565,103,566,431,528,46,429,564,101,526,47,568,98,433,530,44,569,99,434,531,45,567,100,432,529,43,428,108,563,525,39,426,109,561,523,37,427,107,562,524,38,104,424,559,521,42,105,425,560,522,40,106,423,558,520,41,684,681,677,687,57,624,620,623,627,55,635,632,629,631,616,619,56,612,615,651,60,648,644,647,659,58,656,653,655,643,59,640,636,639,608,52,611,605,607,592,53,595,589,591,600,54,603,597,599,51,578,579,573,575,49,584,587,580,583,50,410,545,1,145,698,701,697,700,256,553,373,350,66,254,67,554,371,351,552,65,255,372,352,62,259,556,369,353,63,257,557,370,354,64,258,555,368,355,551,262,72,364,356,549,260,73,362,357,550,261,71,363,358,265,547,68,367,359,263,548,69,365,360,264,546,70,366,361,670,662,671,666,281,246,321,183,467,282,468,247,322,184,245,466,283,320,182,470,280,242,324,186,471,278,243,325,187,469,279,244,323,185,252,287,465,319,189,253,288,463,317,190,251,289,464,318,188,286,248,461,315,192,284,249,462,316,193,285,250,460,314,191,675,682,688,679 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#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 15:16:36 · history