Equation 677 Database

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Magma 5ed5c9bbdc06…

magma 5ed5c9bbdc06
Size
705
Isomorphism class hash
5ed5c9bbdc0678dbf8afbabae2431968f14f4e7186c383f2205f859bca96384f
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 15:59:26
Display reorder
660,151,428,371,582,381,372,426,152,580,379,150,370,581,380,427,431,154,367,585,384,429,155,368,583,382,430,153,369,584,383,434,149,588,377,387,432,147,586,378,385,433,148,587,376,386,373,145,437,591,390,146,435,589,374,388,144,436,590,375,389,678,675,676,682,313,488,213,440,221,214,486,311,438,219,312,215,439,220,487,491,309,212,443,217,489,310,210,441,218,490,308,211,442,216,494,319,446,204,227,492,317,444,205,225,493,318,445,206,226,207,315,497,449,223,316,495,447,208,224,314,496,448,209,222,664,669,671,663,103,464,336,329,346,337,462,104,330,344,102,335,331,345,463,467,106,332,328,349,465,107,333,326,347,466,105,334,327,348,470,101,320,342,352,468,99,321,343,350,469,100,322,341,351,338,97,473,323,355,98,471,324,339,353,96,472,325,340,354,679,684,673,687,73,291,277,393,16,275,292,74,391,17,72,276,392,18,290,294,76,280,396,15,295,77,278,394,13,293,75,279,395,14,289,79,399,283,22,287,80,397,281,23,288,78,398,282,21,652,82,653,657,656,83,286,400,284,19,81,1,401,285,20,704,698,703,700,157,118,558,121,267,556,119,158,122,268,156,557,120,266,117,114,160,561,124,263,115,161,559,125,264,116,159,560,123,265,109,163,127,564,273,110,164,128,562,274,108,162,126,563,272,567,166,112,130,269,167,113,131,565,270,165,111,129,566,271,694,693,692,689,63,570,524,88,416,522,568,64,89,414,65,523,87,415,569,573,62,527,84,419,571,60,525,85,417,572,61,526,86,418,576,69,94,530,422,574,70,95,528,420,575,71,93,529,421,533,68,579,90,425,66,577,91,531,423,67,578,92,532,424,667,665,662,666,5,38,476,452,191,474,36,6,450,189,4,475,451,190,37,41,0,479,455,187,39,2,477,453,188,40,3,478,454,186,44,11,458,482,182,42,12,456,480,180,43,10,457,481,181,485,7,47,461,185,8,45,459,483,183,9,46,460,484,184,695,691,696,690,49,618,642,500,594,640,616,50,498,592,48,641,499,593,617,621,52,645,503,597,619,53,643,501,595,620,51,644,502,596,624,55,506,648,600,622,56,504,646,598,623,54,505,647,599,651,58,627,509,603,59,625,507,649,601,57,626,508,650,602,685,688,683,680,203,536,257,547,358,258,534,201,545,356,202,259,546,357,535,539,199,260,550,361,537,200,261,548,359,538,198,262,549,360,542,194,553,255,364,540,192,551,256,362,541,193,552,254,363,658,197,659,655,654,195,543,554,252,365,196,544,555,253,366,699,701,697,702,33,232,606,240,307,604,233,34,241,305,35,605,242,306,231,228,32,609,243,303,229,30,607,244,304,230,31,608,245,302,238,24,246,612,298,239,25,247,610,296,237,26,248,611,297,615,27,234,249,301,28,235,250,613,299,29,236,251,614,300,661,670,672,668,142,630,512,404,177,510,628,143,402,178,141,511,403,179,629,633,138,515,407,176,631,139,513,405,174,632,140,514,406,175,636,133,410,518,168,634,134,408,516,169,635,132,409,517,170,521,136,639,413,171,137,637,411,519,172,135,638,412,520,173,686,681,674,677 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#2ab683a2f54af56adf82381d164449f2b2adaada784a6acf8eff870c9ce46309, 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 15:59:29 · history