Equation 677 Database

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Magma 65482906c8b7…

magma 65482906c8b7
Size
705
Isomorphism class hash
65482906c8b709ed6d793de4d6fa7fa5da458a9aed3ea6867e822622c197dc8f
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 16:43:56
Display reorder
660,390,378,263,74,4,379,391,261,72,5,380,392,262,73,3,259,393,381,77,1,394,260,382,75,0,383,258,76,395,2,376,254,80,388,10,252,377,78,389,11,253,375,79,387,9,372,257,83,384,6,373,255,81,385,7,374,256,82,386,8,674,685,681,680,402,202,36,204,534,203,403,37,205,535,201,404,38,206,536,39,405,198,207,537,406,40,199,208,538,200,41,209,407,539,193,42,210,400,532,43,194,211,401,533,44,192,212,399,531,196,45,213,396,528,197,46,214,397,529,195,47,215,398,530,670,668,666,672,342,486,274,366,510,487,343,275,367,511,488,344,273,368,512,270,345,489,369,513,346,271,490,370,514,491,272,371,347,515,484,265,364,340,508,266,485,365,341,509,264,483,363,339,507,480,268,360,336,504,481,269,361,337,505,482,267,362,338,506,686,679,678,684,615,616,16,619,614,624,623,17,627,622,632,631,15,635,630,12,639,640,643,638,647,13,648,651,646,656,14,659,655,654,600,22,603,599,598,23,608,611,607,606,21,592,595,591,590,564,18,567,569,568,576,19,579,575,574,584,20,587,583,582,703,701,704,702,426,150,97,129,414,151,427,98,130,415,152,428,96,131,416,100,429,153,128,417,430,101,154,126,418,155,99,127,431,419,148,103,120,424,412,104,149,121,425,413,102,147,122,423,411,144,106,123,420,408,145,107,124,421,409,146,105,125,422,410,690,689,691,693,354,282,162,244,474,283,355,163,245,475,284,356,164,243,476,165,357,285,240,477,358,166,286,241,478,287,167,242,359,479,280,160,250,352,472,161,281,251,353,473,159,279,249,351,471,276,156,246,348,468,277,157,247,349,469,278,158,248,350,470,667,661,665,662,132,114,172,450,227,115,133,173,451,225,116,134,171,452,226,168,135,117,453,223,136,169,118,454,224,119,170,455,137,222,112,178,448,138,218,179,113,449,139,216,177,111,447,140,217,108,174,444,141,221,109,175,445,142,219,110,176,446,143,220,695,692,696,694,230,318,60,558,522,319,228,61,559,523,320,229,62,560,524,63,233,321,561,525,231,64,322,562,526,323,65,563,232,527,316,66,556,236,520,67,317,557,234,521,68,315,555,235,519,312,69,552,239,516,313,70,553,237,517,314,71,554,238,518,687,688,673,677,617,612,182,613,618,620,625,180,621,626,629,633,181,628,634,185,641,636,637,642,649,183,644,645,650,653,184,652,657,658,597,188,596,601,602,186,605,604,609,610,187,589,588,593,594,570,191,571,565,566,572,189,573,577,578,580,190,581,585,586,699,700,697,698,546,88,24,498,330,89,547,25,499,331,87,548,26,500,332,27,549,84,501,333,550,28,85,502,334,86,29,503,551,335,94,30,496,544,328,31,95,497,545,329,32,93,495,543,327,90,33,492,540,324,91,34,493,541,325,92,35,494,542,326,664,669,671,663,438,306,53,294,462,307,439,51,295,463,308,440,52,296,464,49,441,309,297,465,442,50,310,298,466,311,48,299,443,467,304,59,292,436,460,57,305,293,437,461,58,303,291,435,459,300,55,288,432,456,301,56,289,433,457,302,54,290,434,458,683,675,682,676 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#3c7860e7d36dbffc79bc7c2d0a8ff0a692ab326401712ae14ddffd4858b8cd98, 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 16:43:57 · history