Equation 677 Database

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Magma 9f8a6e59d6dc…

magma 9f8a6e59d6dc
Size
705
Isomorphism class hash
9f8a6e59d6dc07eadde0d172ea174d4073eded6a6873705e853cadd7468c9be0
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 16:22:01
Display reorder
704,366,219,234,204,367,205,220,235,368,206,221,236,207,369,218,237,208,370,216,238,209,371,217,239,232,225,364,210,233,226,365,211,231,227,363,212,224,228,360,213,222,229,361,214,223,230,362,215,199,200,198,202,203,201,197,195,192,193,194,196,675,673,674,672,45,512,527,493,46,494,510,525,47,492,511,526,496,44,515,523,497,42,513,524,495,43,514,522,518,507,36,499,516,508,37,500,517,509,38,498,506,521,39,502,504,519,40,503,505,520,41,501,487,488,486,490,491,489,485,483,480,481,482,484,664,666,665,667,250,172,80,156,251,157,173,78,249,158,171,79,159,246,168,83,160,247,169,81,161,248,170,82,75,178,241,162,76,179,242,163,77,177,240,164,174,74,244,165,175,72,245,166,176,73,243,167,648,649,650,651,652,653,654,655,658,656,657,659,685,684,686,687,90,106,110,133,91,134,107,108,92,132,105,109,136,93,102,113,137,94,103,111,135,95,104,112,116,97,88,139,114,98,89,140,115,96,87,138,100,119,84,142,101,117,85,143,99,118,86,141,124,125,123,120,121,122,130,131,128,126,127,129,701,703,700,702,582,373,615,647,583,645,374,616,584,646,372,617,643,585,376,614,644,586,377,612,642,587,375,613,621,379,580,638,622,380,581,636,623,378,579,637,382,620,576,641,383,618,577,639,381,619,578,640,624,625,626,627,628,629,630,631,635,633,634,632,691,690,689,688,62,274,278,301,60,302,275,276,61,300,273,277,304,65,270,281,305,63,271,279,303,64,272,280,284,265,68,307,282,266,66,308,283,264,67,306,268,287,71,310,269,285,69,311,267,286,70,309,292,293,291,288,289,290,298,299,296,294,295,297,662,661,663,660,31,402,417,387,32,388,403,418,30,389,404,419,386,34,405,416,384,35,406,414,385,33,407,415,408,400,29,393,409,401,27,394,410,399,28,395,396,411,25,392,397,412,26,390,398,413,24,391,426,427,428,429,430,431,424,425,422,420,421,423,694,693,695,692,53,608,263,589,51,590,606,261,52,588,607,262,592,49,611,259,593,50,609,260,591,48,610,258,254,603,59,595,252,604,57,596,253,605,58,594,602,257,55,598,600,255,56,599,601,256,54,597,189,190,191,188,186,187,180,181,185,183,184,182,682,683,681,680,150,467,476,446,151,444,465,474,152,445,466,475,449,153,463,479,447,154,464,477,448,155,462,478,471,458,148,452,472,456,149,450,473,457,147,451,461,470,144,455,459,468,145,453,460,469,146,454,438,439,440,441,442,443,436,437,434,432,433,435,696,698,699,697,10,552,567,544,11,545,553,568,9,543,554,569,540,6,555,566,541,7,556,564,542,8,557,565,573,558,0,550,574,559,2,551,575,560,1,549,561,572,4,546,562,570,5,547,563,571,3,548,537,538,539,536,534,535,528,529,533,531,532,530,671,668,670,669,18,325,343,317,19,315,326,344,20,316,324,342,313,21,328,346,314,22,329,347,312,23,327,345,341,331,16,323,339,332,17,321,340,330,15,322,334,337,12,319,335,338,13,320,333,336,14,318,356,354,355,359,357,358,351,352,349,350,348,353,676,678,677,679 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#2e8e4ac0a437874a6303a2bb1c968f3f1df955f15fe5de36e1349d884d5d267c, 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 16:22:02 · history