Equation 677 Database

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Magma e3e8756eac68…

magma e3e8756eac68
Size
705
Isomorphism class hash
e3e8756eac68352c694bf41568c7a0fe3fecda7a5a6c57808819929fea5ba97d
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 20:04:33
Display reorder
660,347,350,349,345,355,353,354,352,0,351,346,348,547,545,546,544,549,548,551,550,552,553,555,554,540,541,543,542,532,533,535,534,536,537,539,538,570,569,568,571,574,573,572,575,578,576,577,579,564,566,565,567,557,558,556,559,561,562,560,563,684,683,682,681,11,10,12,9,7,8,2,1,3,4,5,6,368,369,370,371,373,375,372,374,377,379,376,378,364,367,365,366,356,359,357,358,360,363,361,362,394,392,395,393,398,396,399,397,402,401,403,400,389,390,391,388,380,382,383,381,384,386,387,385,667,665,666,668,100,102,101,98,99,97,93,91,92,96,94,95,268,54,304,316,52,317,269,305,53,318,270,306,50,315,267,303,51,313,265,301,49,314,266,302,310,45,322,274,311,43,323,275,312,44,324,276,48,309,321,273,46,307,319,271,47,308,320,272,676,674,675,673,173,172,174,171,169,170,163,164,165,166,167,168,260,339,37,178,337,179,261,38,338,180,262,39,342,177,259,40,340,175,257,41,341,176,258,42,636,639,637,638,645,647,644,646,652,655,653,654,635,633,632,634,343,183,181,263,344,184,182,264,697,698,699,700,114,113,112,109,110,111,104,105,103,107,108,106,224,201,213,189,202,190,225,214,200,188,226,212,197,185,223,209,198,186,221,210,199,187,222,211,219,207,195,230,220,208,196,231,218,206,194,232,203,215,191,229,204,216,192,227,205,217,193,228,692,689,690,691,34,36,35,32,33,31,27,25,26,30,28,29,328,292,280,66,293,64,329,281,294,65,330,282,291,62,327,279,289,63,325,277,290,61,326,278,286,298,57,334,287,299,55,335,288,300,56,336,297,285,60,333,295,283,58,331,296,284,59,332,661,663,662,664,250,249,248,245,246,247,255,256,254,251,252,253,117,141,160,136,139,137,115,161,140,138,116,162,144,135,120,159,142,133,118,157,143,134,119,158,151,147,127,123,152,145,128,121,153,146,129,122,150,154,130,126,148,155,131,124,149,156,132,125,696,695,693,694,69,68,67,71,72,70,74,75,73,77,78,76,595,594,593,592,598,596,599,597,602,600,603,601,590,589,591,588,582,580,583,581,586,584,587,585,616,618,617,619,620,622,621,623,624,626,625,627,614,613,612,615,606,604,605,607,610,608,609,611,685,686,688,687,23,22,24,21,19,20,13,14,15,16,17,18,422,421,423,420,425,424,426,427,428,429,430,431,416,417,418,419,409,408,410,411,413,412,414,415,643,641,640,642,651,649,648,650,659,656,657,658,629,631,628,630,433,435,432,434,405,407,404,406,701,702,704,703,90,89,88,85,86,87,80,81,79,83,84,82,499,497,498,496,501,500,503,502,505,504,507,506,492,493,495,494,485,484,487,486,489,488,491,490,522,520,521,523,526,524,525,527,530,528,529,531,517,518,516,519,508,510,509,511,512,514,513,515,670,672,671,669,244,243,242,239,240,241,234,235,233,237,238,236,449,448,450,451,452,455,453,454,456,459,457,458,445,447,444,446,436,439,437,438,440,443,441,442,474,473,475,472,478,477,479,476,482,480,483,481,468,470,471,469,461,462,463,460,465,466,467,464,677,678,679,680 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#b8dd5d8f5072bb4839777555438d548fef97075a280814a177ddbc224cea50a0, 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 20:04:34 · history