Equation 677 Database

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Magma 5900caf6630e…

magma 5900caf6630e
Size
705
Isomorphism class hash
5900caf6630e5fb89a3bd9f7e7003a56ad40dd2e9921307f13a77e8ebaa54650
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 20:38:17
Display reorder
660,546,198,24,479,354,544,199,22,477,355,545,197,23,478,356,194,542,20,475,353,195,543,21,476,351,196,541,19,474,352,552,15,189,485,345,550,13,190,483,346,551,14,188,484,347,18,548,192,481,348,16,549,193,482,349,17,547,191,480,350,678,687,683,681,249,78,287,273,261,250,79,285,274,262,251,77,286,275,263,74,252,290,276,264,75,253,288,277,265,76,254,289,278,266,255,293,69,279,267,256,291,70,280,268,257,292,68,281,269,296,258,72,282,270,294,259,73,283,271,295,260,71,284,272,668,672,664,670,577,87,361,436,149,575,88,362,434,150,576,86,360,435,151,90,573,357,432,148,91,574,358,433,146,89,572,359,431,147,583,367,85,442,140,581,368,83,440,141,582,366,84,441,142,363,579,81,438,143,364,580,82,439,144,365,578,80,437,145,677,679,685,674,472,225,414,240,398,470,226,412,241,396,471,224,413,242,397,228,468,417,239,394,229,469,415,237,395,227,467,416,238,393,657,655,231,653,654,641,639,232,636,638,649,647,230,644,646,620,622,234,624,625,631,633,235,628,630,418,473,233,236,399,703,697,701,704,558,112,448,208,589,556,110,446,206,587,557,111,447,207,588,115,554,444,211,585,113,555,445,209,586,114,553,443,210,584,564,454,107,203,595,562,452,108,204,593,563,453,109,205,594,450,560,106,202,591,451,561,104,200,592,449,559,105,201,590,691,693,692,690,424,158,382,460,322,422,159,383,458,323,423,160,381,459,321,161,420,385,456,325,162,421,386,457,326,163,419,384,455,324,430,388,156,466,328,428,389,157,464,329,429,387,155,465,327,391,426,152,462,331,392,427,153,463,332,390,425,154,461,330,663,666,662,669,129,52,116,220,305,130,53,117,218,303,128,54,118,219,304,51,132,119,223,308,49,133,120,221,306,50,131,121,222,307,135,122,58,215,300,136,123,59,216,301,134,124,60,217,302,125,138,57,214,299,126,139,55,212,297,127,137,56,213,298,694,695,696,689,373,314,405,27,613,374,312,403,25,611,372,313,404,26,612,310,369,401,30,609,311,370,402,28,610,309,371,400,29,608,379,411,320,33,619,380,409,318,31,617,378,410,319,32,618,407,375,316,36,615,408,376,317,34,616,406,377,315,35,614,676,688,673,675,245,0,567,67,515,243,2,565,65,513,244,3,566,66,514,4,248,570,63,511,5,246,568,64,512,6,247,569,62,510,652,659,7,656,658,637,643,8,640,642,645,651,9,648,650,627,626,10,621,623,635,629,11,632,634,571,1,12,61,516,699,702,700,698,491,103,601,39,534,489,101,599,37,532,490,102,600,38,533,99,487,597,42,530,100,488,598,40,531,98,486,596,41,529,497,607,94,45,540,495,605,92,43,538,496,606,93,44,539,603,493,97,48,536,604,494,95,46,537,602,492,96,47,535,661,667,665,671,164,334,503,522,177,165,335,501,520,178,166,333,502,521,176,337,167,499,518,180,338,168,500,519,181,336,169,498,517,179,170,509,340,528,183,171,507,341,526,184,172,508,339,527,182,505,173,343,524,186,506,174,344,525,187,504,175,342,523,185,682,686,684,680 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#c84e71ca0bd6781f4c1c1e66d375057eb5ddb823e6cd89140cc4ca3da0f421d2, 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 20:38:18 · history