Equation 677 Database

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Magma 050f3a65b88f…

magma 050f3a65b88f
Size
705
Isomorphism class hash
050f3a65b88f07d047e05090aca8516c39514c747ed38d3a6a7cd6577b8d0a5b
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 16:42:48
Display reorder
660,295,423,228,555,399,296,556,424,229,400,425,557,294,230,401,554,298,422,231,398,552,299,420,232,396,553,297,421,233,397,414,546,234,293,390,415,547,235,291,391,416,548,236,292,392,549,417,237,289,393,550,418,238,290,394,551,419,239,288,395,679,677,685,687,99,363,343,483,138,100,484,364,344,139,365,485,101,342,140,482,98,362,346,141,480,96,360,347,142,481,97,361,345,143,354,474,349,105,136,355,475,350,106,137,356,476,348,107,135,477,357,352,104,132,478,358,353,102,133,479,359,351,103,134,664,662,667,669,242,495,309,519,196,240,520,496,310,197,497,521,241,311,195,518,245,494,308,192,516,243,492,306,193,517,244,493,307,194,486,510,300,248,202,487,511,301,246,203,488,512,302,247,201,513,489,303,251,198,514,490,304,249,199,515,491,305,250,200,683,688,684,673,45,636,638,637,643,46,644,645,646,651,653,652,47,654,659,629,48,628,630,635,612,49,613,614,619,621,50,620,622,627,41,14,43,51,587,39,12,44,52,585,40,13,42,53,586,588,589,590,54,592,597,596,598,55,603,605,604,606,56,611,697,704,698,700,71,471,179,375,531,69,376,472,177,532,473,377,70,178,533,374,74,470,175,530,372,72,468,176,528,373,73,469,174,529,462,366,170,77,522,463,367,168,75,523,464,368,169,76,524,369,465,173,80,525,370,466,171,78,526,371,467,172,79,527,693,694,690,689,205,582,268,254,507,206,252,583,269,508,584,253,204,267,509,257,208,581,264,506,255,209,579,265,504,256,207,580,266,505,573,260,274,211,498,574,258,275,212,499,575,259,273,210,500,263,576,270,214,501,261,577,271,215,502,262,578,272,213,503,672,668,671,666,191,2,82,108,543,189,109,1,83,544,0,110,190,81,545,111,187,5,85,542,112,188,3,86,540,113,186,4,84,541,8,114,88,182,534,6,115,89,180,535,7,116,87,181,536,117,11,91,185,537,118,9,92,183,538,119,10,90,184,539,691,695,692,696,32,411,567,447,435,30,448,412,568,436,413,449,31,569,437,446,28,410,566,434,444,29,408,564,432,445,27,409,565,433,402,438,558,38,426,403,439,559,36,427,404,440,560,37,428,441,405,561,34,429,442,406,562,35,430,443,407,563,33,431,678,680,681,686,130,642,641,640,639,131,648,650,649,647,658,656,129,657,655,632,126,634,633,631,616,127,618,617,615,624,128,626,625,623,570,313,317,121,94,571,314,315,122,95,572,312,316,120,93,593,595,594,124,591,600,602,601,125,599,608,610,609,123,607,701,703,702,699,22,147,327,65,166,23,63,148,328,167,149,64,21,329,165,68,25,146,326,162,66,26,144,324,163,67,24,145,325,164,153,60,318,20,157,154,61,319,18,158,155,62,320,19,156,59,152,321,16,160,57,150,322,17,161,58,151,323,15,159,661,665,670,663,227,459,387,280,339,225,281,460,388,340,461,279,226,389,341,276,223,458,386,338,277,224,456,384,336,278,222,457,385,337,450,286,378,218,330,451,287,379,216,331,452,285,380,217,332,282,453,381,221,333,283,454,382,219,334,284,455,383,220,335,682,675,674,676 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#3a4a415766bc24344b8990a318a493c1fb50830922fededbbeb9b2ef7d49358b, 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 16:42:49 · history