Equation 677 Database

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Magma 804cef6dccbd…

magma 804cef6dccbd
Size
705
Isomorphism class hash
804cef6dccbdee2d8d2745d9f8924ee0e432108445ce77242acdb2ff41b34654
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 15:58:26
Display reorder
660,9,395,366,352,298,10,396,364,353,299,11,394,365,354,300,391,8,362,351,297,392,6,363,349,295,393,7,361,350,296,1,401,357,343,304,0,402,355,344,305,2,400,356,345,306,397,3,360,346,303,398,4,358,347,301,399,5,359,348,302,664,670,672,661,194,479,97,92,41,192,480,98,93,42,193,478,99,91,40,475,197,100,95,37,476,195,101,96,38,477,196,102,94,39,189,485,103,90,47,190,486,104,88,48,191,484,105,89,46,481,188,106,86,43,482,186,107,87,44,483,187,108,85,45,686,690,688,689,321,585,431,256,383,319,586,432,257,384,320,584,430,258,382,581,324,427,255,379,582,322,428,253,380,583,323,429,254,381,327,591,437,247,389,325,592,438,248,390,326,590,436,249,388,587,330,433,250,385,588,328,434,251,386,589,329,435,252,387,671,665,663,667,209,503,419,455,116,207,504,420,456,117,208,502,418,454,115,499,205,415,451,119,500,206,416,452,120,501,204,417,453,118,200,509,425,461,114,198,510,426,462,112,199,508,424,460,113,505,203,421,457,110,506,201,422,458,111,507,202,423,459,109,679,675,683,677,126,527,211,467,551,124,528,212,468,552,125,526,210,466,550,523,122,214,463,547,524,123,215,464,548,525,121,213,465,549,132,533,217,473,557,130,534,218,474,558,131,532,216,472,556,529,128,220,469,553,530,129,221,470,554,531,127,219,471,555,668,662,669,666,368,315,491,27,443,369,313,492,28,444,367,314,490,26,442,318,371,487,32,439,316,372,488,34,440,317,370,489,31,441,374,310,497,21,449,375,311,498,22,450,373,312,496,20,448,309,377,493,24,445,307,378,494,25,446,308,376,495,23,447,693,696,695,694,135,559,568,597,145,133,634,635,632,633,134,560,567,596,146,562,138,564,593,148,563,136,565,594,149,561,137,566,595,147,141,652,653,654,655,139,656,657,658,659,140,648,649,650,651,636,144,637,638,639,640,142,641,642,643,645,143,644,646,647,701,702,704,703,158,229,228,602,65,156,230,226,603,66,157,231,227,601,64,232,161,224,598,61,233,159,225,599,62,234,160,223,600,63,153,629,628,608,71,154,631,630,609,72,155,627,626,607,70,36,152,222,604,67,623,150,622,605,68,625,151,624,606,69,700,699,697,698,30,288,614,573,407,33,286,615,574,408,35,287,613,572,406,284,29,610,569,403,285,18,611,570,404,283,19,612,571,405,12,294,620,579,413,13,292,621,580,414,14,293,619,578,412,290,15,616,575,409,291,16,617,576,410,289,17,618,577,411,678,684,674,682,84,179,539,242,163,82,177,540,243,164,83,178,538,241,162,175,80,535,245,166,176,81,536,246,167,174,79,537,244,165,75,185,545,240,169,73,183,546,238,170,74,184,544,239,168,181,78,541,236,172,182,76,542,237,173,180,77,543,235,171,680,681,673,676,59,515,269,331,276,60,516,270,332,274,58,514,268,333,275,511,55,265,334,272,512,56,266,335,273,513,57,267,336,271,50,521,260,337,282,51,522,261,338,280,49,520,259,339,281,517,53,263,340,278,518,54,264,341,279,519,52,262,342,277,687,685,691,692 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#299bf89dcaadd64e33422b05a87b398de7449d556bda64ba0ca787ebaa3d1bcb, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 15:58:28 · history