Equation 677 Database

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Magma e5cdd8ff2364…

magma e5cdd8ff2364
Size
705
Isomorphism class hash
e5cdd8ff2364a5e4d1c8fcd974837be45e4cf4f509b28a259fd1e6b67d9b60ea
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 15:15:24
Display reorder
660,471,128,343,490,491,472,129,344,493,492,130,488,470,342,489,474,131,339,496,497,475,132,340,499,498,473,133,341,494,495,126,469,349,487,486,127,467,350,483,482,125,468,348,485,484,122,465,345,479,478,123,466,346,480,481,124,464,347,477,476,682,673,684,683,6,139,211,225,94,4,137,209,226,92,138,227,5,210,93,2,135,207,228,97,3,136,208,229,95,0,134,206,230,96,145,12,217,223,89,143,10,215,224,90,144,11,216,222,91,141,8,213,219,88,142,9,214,220,86,140,7,212,221,87,665,666,670,669,358,32,310,444,370,359,33,311,445,371,31,443,357,309,369,361,35,313,447,373,362,36,314,448,374,360,34,312,446,372,30,356,308,442,368,28,354,306,440,366,29,355,307,441,367,26,352,304,438,364,27,353,305,439,365,25,351,303,437,363,675,674,676,680,625,119,624,620,623,633,120,632,629,631,121,612,617,616,615,649,118,648,644,647,657,116,656,653,655,641,117,640,636,639,110,609,608,605,607,111,593,592,589,591,112,601,600,597,599,113,575,574,576,577,114,585,584,580,583,115,461,400,1,399,699,697,704,703,296,109,167,334,171,294,107,168,335,172,108,333,295,169,170,292,105,166,337,174,293,106,164,338,175,291,104,165,336,173,100,302,158,332,177,98,300,159,330,178,99,301,160,331,176,103,298,161,328,180,101,299,162,329,181,102,297,163,327,179,689,691,694,690,394,18,420,151,249,395,16,421,149,250,17,150,393,419,251,397,14,423,147,252,398,15,424,148,253,396,13,422,146,254,24,392,418,157,247,22,390,416,155,248,23,391,417,156,246,20,388,414,153,243,21,389,415,154,244,19,387,413,152,245,662,663,672,671,563,71,562,60,187,564,72,565,58,185,70,59,561,560,186,569,67,568,56,183,570,68,571,57,184,567,69,566,55,182,62,558,559,51,193,63,554,555,49,191,61,556,557,50,192,65,550,551,54,189,66,553,552,52,190,64,548,549,53,188,695,696,693,692,538,46,539,456,382,541,47,540,457,383,48,455,536,537,381,544,45,545,459,385,547,43,546,460,386,542,44,543,458,384,37,535,534,454,380,38,531,530,452,378,39,533,532,453,379,40,527,526,450,376,41,528,529,451,377,42,525,524,449,375,685,686,677,681,626,196,627,621,622,634,194,635,628,630,195,613,618,619,614,650,199,651,645,646,658,197,659,652,654,642,198,643,637,638,202,611,610,606,604,200,594,595,590,588,201,603,602,598,596,205,578,579,573,572,203,586,587,582,581,204,462,463,73,218,701,702,700,698,432,235,326,514,515,433,236,324,516,517,234,512,431,325,513,435,231,322,520,521,436,232,323,522,523,434,233,321,518,519,241,430,317,511,510,242,428,315,506,507,240,429,316,509,508,237,426,320,503,502,238,427,318,505,504,239,425,319,501,500,664,661,667,668,270,79,408,280,257,271,77,409,281,255,78,279,272,407,256,269,75,411,283,260,267,76,412,284,258,268,74,410,282,259,85,276,406,286,263,83,277,404,287,261,84,278,405,285,262,81,275,402,289,266,82,273,403,290,264,80,274,401,288,265,678,679,688,687 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#0d8cdfdeb3c53efefcd572d9bf5ad220efd26f91f8a2b4cfd66b53f1dccf6eeb, 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 15:15:26 · history