Equation 677 Database

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Magma 9b5e436eab6a…

magma 9b5e436eab6a
Size
705
Isomorphism class hash
9b5e436eab6a1b8f33462b7eadd7bb57ac2f9020ebf23141ab054b8734476d6d
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 19:13:11
Display reorder
660,364,174,379,130,511,128,365,175,380,512,173,129,366,381,513,133,367,170,378,510,131,368,171,376,508,132,369,172,377,509,370,165,385,136,517,371,166,386,134,518,372,164,387,135,519,373,168,384,139,516,374,169,382,137,514,375,167,383,138,515,674,680,681,676,419,308,293,224,321,225,420,309,294,319,307,226,421,292,320,227,418,304,296,317,228,416,305,297,318,229,417,306,295,316,425,314,299,230,327,426,315,300,231,325,427,313,298,232,326,424,310,302,233,323,422,311,303,234,324,423,312,301,235,322,667,672,662,663,250,331,407,146,243,147,248,332,408,244,333,148,249,409,242,149,253,330,406,246,150,251,328,404,247,151,252,329,405,245,256,337,413,144,241,254,338,414,145,239,255,339,415,143,240,259,336,412,140,237,257,334,410,141,238,258,335,411,142,236,673,685,687,677,277,455,390,21,622,22,278,456,388,620,457,23,279,389,621,20,276,454,393,625,18,274,452,391,623,19,275,453,392,624,638,640,637,12,643,646,648,644,13,651,654,656,652,14,659,629,630,628,15,632,272,458,394,16,626,273,459,395,17,627,700,701,698,697,99,104,523,183,431,184,100,105,524,432,106,182,98,525,433,186,102,107,522,430,187,103,108,520,428,185,101,109,521,429,97,110,529,181,437,95,111,530,179,438,96,112,531,180,439,93,113,528,177,436,94,114,526,178,434,92,115,527,176,435,689,691,694,695,67,81,70,260,555,261,65,82,68,556,80,262,66,69,557,263,63,84,73,554,264,64,85,71,552,265,62,83,72,553,58,87,76,266,561,56,88,74,267,562,57,86,75,268,563,61,90,79,269,560,59,91,77,270,558,60,89,78,271,559,669,668,661,666,27,343,487,201,463,202,28,344,488,464,345,200,29,489,465,204,26,342,486,462,205,24,340,484,460,203,25,341,485,461,33,349,493,207,469,34,350,494,208,470,35,351,495,206,471,32,348,492,210,468,30,346,490,211,466,31,347,491,209,467,690,692,696,693,55,2,475,163,355,161,53,1,476,356,0,162,54,477,357,159,51,5,474,354,160,52,3,472,352,158,50,4,473,353,46,8,481,154,361,44,6,482,152,362,45,7,483,153,363,49,11,480,157,360,47,9,478,155,358,48,10,479,156,359,679,675,683,678,547,40,399,218,567,219,548,41,400,568,42,220,549,401,569,221,546,39,398,566,222,544,37,396,564,223,545,38,397,565,641,636,639,216,642,649,645,647,217,650,657,653,655,215,658,635,633,634,212,631,550,43,402,213,570,551,36,403,214,571,702,704,703,699,575,443,499,288,599,286,576,444,500,600,445,287,577,501,601,291,574,442,498,598,289,572,440,496,596,290,573,441,497,597,581,449,505,283,605,582,450,506,284,606,583,451,507,285,607,580,448,504,282,604,578,446,502,280,602,579,447,503,281,603,664,671,670,665,188,587,611,117,535,118,189,588,612,536,589,116,190,613,537,120,191,586,610,534,121,192,584,608,532,119,193,585,609,533,194,593,617,123,541,195,594,618,124,542,196,595,619,122,543,197,592,616,126,540,198,590,614,127,538,199,591,615,125,539,686,682,684,688 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#90fd68087a2f09648803d65723dcc8788b62f036d4e0ed1478893fb37d6a20cd, 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 19:13:12 · history