Equation 677 Database

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Magma 95c33f448a4f…

magma 95c33f448a4f
Size
705
Isomorphism class hash
95c33f448a4fecc57c1ac347784a630e65ef64a2e4ae3be2d64c3b80fbf79b79
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 17:19:12
Display reorder
660,457,418,445,587,527,458,419,446,588,528,459,420,447,589,529,421,456,444,586,526,422,454,442,584,524,423,455,443,585,525,436,448,416,578,518,437,449,417,579,519,438,450,415,580,520,451,439,412,581,521,452,440,413,582,522,453,441,414,583,523,671,667,663,661,155,61,144,132,515,156,62,142,130,516,154,63,143,131,517,64,151,140,128,514,65,152,141,129,512,66,153,139,127,513,135,146,67,123,506,133,147,68,121,507,134,145,69,122,508,149,138,70,126,509,150,136,71,124,510,148,137,72,125,511,690,687,688,685,191,338,180,539,503,192,339,178,540,504,190,337,179,541,505,334,194,183,538,502,335,195,181,536,500,336,193,182,537,501,186,197,329,530,494,184,198,330,531,495,185,196,328,532,496,200,189,332,533,497,201,187,333,534,498,199,188,331,535,499,668,666,664,669,575,82,20,2,551,576,83,21,3,552,577,84,19,0,553,81,574,23,5,550,79,572,24,6,548,80,573,22,4,549,18,566,73,8,542,16,567,74,9,543,17,568,75,7,544,569,14,76,11,545,570,15,77,12,546,571,13,78,10,547,674,679,680,682,563,251,481,611,111,564,249,482,612,109,565,250,483,613,110,254,562,480,610,114,252,560,478,608,112,253,561,479,609,113,472,554,257,602,117,473,555,255,603,115,474,556,256,604,116,557,475,260,605,120,558,476,258,606,118,559,477,259,607,119,672,662,670,665,599,168,469,409,433,600,166,470,410,434,601,167,471,411,435,171,598,468,408,432,169,596,466,406,430,170,597,467,407,431,460,590,174,400,424,461,591,172,401,425,462,592,173,402,426,593,463,177,403,427,594,464,175,404,428,595,465,176,405,429,694,695,698,696,490,36,647,238,245,654,34,655,653,652,658,35,659,656,657,32,491,646,247,164,33,492,644,248,165,31,493,645,246,163,638,488,27,244,159,639,489,25,242,157,640,487,26,243,158,484,641,30,240,162,485,642,28,241,160,486,643,29,239,161,702,703,701,704,267,290,225,1,237,648,291,223,649,235,650,289,224,651,236,286,268,221,271,233,287,269,222,272,234,288,270,220,273,232,216,265,281,278,228,214,266,282,279,226,215,264,280,277,227,261,219,284,274,231,262,217,285,275,229,263,218,283,276,230,699,697,700,693,364,108,354,390,378,365,106,352,388,376,366,107,353,389,377,104,367,357,393,381,105,368,355,391,379,103,369,356,392,380,360,370,99,396,384,358,371,97,394,382,359,372,98,395,383,373,363,102,399,387,374,361,100,397,385,375,362,101,398,386,676,675,673,684,326,53,308,297,635,327,54,309,295,636,325,52,307,296,637,49,322,304,293,634,50,323,305,294,632,51,324,306,292,633,314,317,59,303,626,315,318,60,301,627,313,316,58,302,628,320,310,55,299,629,321,311,56,300,630,319,312,57,298,631,677,683,678,681,348,211,623,44,93,346,212,624,45,91,347,213,625,43,92,210,351,622,47,96,208,349,620,48,94,209,350,621,46,95,614,343,202,42,88,615,344,203,40,89,616,345,204,41,90,342,617,205,38,87,340,618,206,39,85,341,619,207,37,86,686,691,689,692 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#4dbd6b0006d3996c22611f6a9a74b6d8666415e8467cb95ff3380ed5b17e9234, 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 17:19:13 · history