Equation 677 Database

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Magma de825caf5ca9…

magma de825caf5ca9
Size
705
Isomorphism class hash
de825caf5ca9ec60d4597725f320b445b37a71b1468a8f33b9340c3ebc265906
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 16:26:14
Display reorder
660,524,389,455,293,395,522,387,453,291,393,523,388,454,292,394,385,520,451,289,391,386,521,452,290,392,519,384,450,288,390,530,284,380,461,401,528,282,378,459,399,529,283,379,460,400,287,526,383,457,397,285,527,381,458,398,286,525,382,456,396,677,680,678,682,220,134,214,50,136,221,135,215,48,137,222,133,216,49,138,130,223,217,46,139,131,224,218,47,140,225,132,219,45,141,226,56,125,212,142,227,54,126,213,143,228,55,124,211,144,52,229,128,208,145,53,230,129,209,146,51,231,127,210,147,664,668,663,671,160,335,156,60,431,161,333,154,61,429,162,334,155,62,430,331,163,159,59,427,332,164,157,57,428,165,330,158,58,426,166,66,341,151,437,167,67,339,152,435,168,68,340,153,436,65,169,337,150,433,63,170,338,148,434,64,171,336,149,432,679,674,676,683,464,42,123,186,533,462,43,121,184,531,463,44,122,185,532,41,467,119,189,536,39,465,120,187,534,466,40,118,188,535,652,192,654,653,657,636,190,638,637,641,644,191,646,645,649,195,620,621,624,625,193,629,630,628,633,194,468,38,117,537,698,697,704,703,311,419,443,299,75,309,417,441,297,76,310,418,442,298,77,415,307,439,295,78,416,308,440,296,79,306,414,438,294,80,317,305,425,449,73,315,303,423,447,74,316,304,424,448,72,301,313,421,445,69,302,314,422,446,70,300,312,420,444,71,689,691,690,693,481,177,574,36,323,479,175,572,37,321,480,176,573,35,322,173,477,570,32,319,174,478,571,33,320,476,172,569,34,318,487,27,183,580,329,485,28,181,578,327,486,26,182,579,328,30,483,179,576,325,31,484,180,577,326,29,482,178,575,324,662,672,670,666,247,267,607,6,606,248,265,602,1,603,249,266,604,5,605,263,246,0,13,269,264,244,601,9,600,245,262,2,11,268,253,19,258,619,618,254,14,256,614,615,255,16,257,616,617,25,252,261,610,611,20,250,259,613,612,22,251,260,608,609,695,696,694,692,376,593,356,272,350,377,591,354,270,348,375,592,355,271,349,589,372,359,275,353,590,373,357,273,351,374,588,358,274,352,367,278,599,362,345,368,276,597,360,346,366,277,598,361,347,281,370,595,365,344,279,371,596,363,342,280,369,594,364,343,675,685,687,673,473,493,567,3,586,474,491,565,4,584,475,492,566,7,585,489,472,563,8,582,490,470,564,10,583,471,488,562,12,581,655,15,656,658,659,639,17,640,642,643,647,18,648,650,651,21,626,627,622,623,23,631,632,634,635,24,469,494,568,587,702,701,700,699,407,512,106,207,543,405,510,107,205,541,406,511,105,206,542,508,403,109,203,539,509,404,110,204,540,402,507,108,202,538,413,198,518,112,549,411,196,516,113,547,412,197,517,111,548,201,409,514,115,545,199,410,515,116,546,200,408,513,114,544,669,661,667,665,102,500,83,237,555,103,498,81,235,553,104,499,82,236,554,496,101,86,233,551,497,99,84,234,552,100,495,85,232,550,93,243,506,89,561,94,241,504,87,559,95,242,505,88,560,239,96,502,92,557,240,97,503,90,558,238,98,501,91,556,684,686,681,688 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#31b39e995794136cb14e9cfb9c49dab141b331fe9ae7acf51f9a6bc9a2946638, 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 16:26:16 · history