Equation 677 Database

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Magma 3aa235e194ea…

magma 3aa235e194ea
Size
705
Isomorphism class hash
3aa235e194ea7ab90e5563b5888520e0d885c124150a7254e496f4862a6dfb79
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 20:41:24
Display reorder
660,136,367,545,391,521,137,365,543,389,519,135,366,544,390,520,363,139,541,387,517,364,140,542,388,518,362,138,540,386,516,536,358,382,142,512,534,356,380,143,510,535,357,381,141,511,361,539,385,145,515,359,537,383,146,513,360,538,384,144,514,685,683,675,676,331,586,86,256,16,329,584,84,254,17,330,585,85,255,15,582,327,82,259,19,583,328,83,257,20,581,326,81,258,18,77,577,251,322,22,75,575,252,320,23,76,576,253,321,21,580,80,250,325,25,578,78,248,323,26,579,79,249,324,24,666,672,670,668,10,403,509,343,154,11,401,507,341,155,9,402,508,342,153,399,13,505,339,157,400,14,506,340,158,398,12,504,338,156,500,394,334,8,152,498,392,332,6,150,499,393,333,7,151,397,503,337,4,148,395,501,335,5,149,396,502,336,3,147,682,686,677,673,43,654,653,655,659,44,638,637,639,643,42,646,645,647,651,622,39,621,623,627,630,40,628,631,635,614,41,613,615,619,226,1,233,49,601,224,0,231,50,599,225,2,232,48,600,605,604,606,45,608,229,227,234,46,602,230,228,235,47,603,704,697,698,700,288,90,439,65,116,289,91,437,63,114,287,92,438,64,115,89,284,435,68,112,87,285,436,66,113,88,286,434,67,111,430,96,71,294,122,428,97,69,295,120,429,98,70,293,121,95,433,74,290,118,93,431,72,291,119,94,432,73,292,117,691,694,692,689,32,183,562,57,174,30,184,560,58,175,31,185,561,59,176,186,28,558,60,173,187,29,559,61,171,188,27,557,62,172,553,189,55,38,180,551,190,56,36,181,552,191,54,37,182,192,556,51,34,179,193,554,52,35,177,194,555,53,33,178,669,663,661,665,100,302,217,379,344,101,303,218,377,345,99,304,216,378,346,305,103,213,375,347,306,104,214,376,348,307,102,215,374,349,208,300,370,106,350,209,301,368,107,351,207,299,369,105,352,296,211,373,109,353,297,212,371,110,354,298,210,372,108,355,693,696,695,690,123,415,533,170,574,124,413,531,168,572,125,414,532,169,573,411,126,529,166,570,412,127,530,167,571,410,128,528,165,569,524,406,161,129,565,522,404,159,130,563,523,405,160,131,564,409,527,164,132,568,407,525,162,133,566,408,526,163,134,567,684,687,678,674,319,658,656,652,657,317,642,640,636,641,318,650,648,644,649,626,315,624,620,625,634,316,632,629,633,618,314,616,612,617,490,548,221,310,495,488,546,222,308,493,489,547,223,309,494,611,610,609,313,607,549,491,220,311,496,550,492,219,312,497,699,701,703,702,247,274,475,451,269,245,272,473,449,270,246,273,474,450,271,277,243,471,447,268,275,244,472,448,266,276,242,470,446,267,466,280,442,238,260,464,278,440,236,261,465,279,441,237,262,283,469,445,241,263,281,467,443,239,264,282,468,444,240,265,664,671,667,662,197,487,427,598,463,195,485,425,596,461,196,486,426,597,462,483,200,423,594,459,484,198,424,595,460,482,199,422,593,458,418,478,589,203,454,416,476,587,201,452,417,477,588,202,453,481,421,592,206,457,479,419,590,204,455,480,420,591,205,456,679,680,681,688 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#cb899e6f30effddffe30366e2e9dc963aa0ce854a3a9ff04422e3e195000d2a8, 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 20:41:24 · history