Equation 677 Database

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Magma b114547dbe17…

magma b114547dbe17
Size
705
Isomorphism class hash
b114547dbe17b57ec374f798878edb4ff944badbe13fbf2e866cb0dc60457c5a
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 15:23:13
Display reorder
660,373,113,255,527,386,374,256,525,384,114,372,115,257,526,385,112,369,258,523,382,110,370,259,524,383,111,371,260,522,381,253,379,119,533,392,380,120,531,254,390,378,121,532,252,391,118,375,529,249,388,116,376,530,250,389,117,377,528,251,387,682,675,676,686,190,230,169,216,201,191,170,217,202,228,189,229,168,218,203,226,193,165,215,204,227,194,166,213,205,225,192,167,214,206,175,196,236,222,207,197,234,223,176,208,195,235,224,174,209,232,199,221,171,210,233,200,219,172,211,231,198,220,173,212,670,672,668,663,484,33,96,558,237,482,97,556,238,34,483,32,95,557,239,36,480,92,554,240,37,481,93,555,241,35,479,94,553,242,87,490,45,564,243,488,47,562,88,244,489,48,563,86,245,42,486,560,90,246,39,487,561,91,247,40,485,559,89,248,684,673,680,677,520,477,283,395,615,518,284,393,613,475,519,476,282,394,614,473,516,279,398,618,474,517,280,396,616,472,515,281,397,617,274,657,656,654,659,641,640,638,275,643,649,648,646,273,651,622,623,620,277,624,632,633,630,278,635,478,521,399,276,619,704,698,701,700,417,272,123,362,349,415,124,360,350,270,416,271,122,361,348,268,413,126,358,345,269,414,127,359,346,267,412,125,357,347,129,423,263,368,355,421,261,366,130,356,422,262,367,128,354,266,419,364,132,351,264,420,365,133,352,265,418,363,131,353,691,690,693,689,546,338,66,29,465,544,67,30,463,336,545,337,65,31,464,334,542,62,28,461,335,543,63,26,462,333,541,64,27,460,72,552,344,20,471,550,342,21,73,469,551,343,22,71,470,340,548,23,68,467,341,549,24,69,468,339,547,25,70,466,661,665,669,662,300,59,77,150,405,301,78,151,403,60,302,61,79,149,404,58,299,76,146,401,56,297,74,147,402,57,298,75,148,400,83,306,50,156,411,307,51,157,84,409,308,52,155,85,410,53,305,152,82,407,54,303,153,80,408,55,304,154,81,406,695,692,696,694,453,326,107,312,594,451,108,313,592,324,452,325,109,314,593,322,449,106,311,590,323,450,104,309,591,321,448,105,310,589,98,459,332,318,600,457,330,319,99,598,458,331,320,100,599,328,455,317,101,596,329,456,315,102,597,327,454,316,103,595,683,687,679,674,2,162,16,539,12,3,19,537,8,163,4,161,14,538,10,158,5,9,535,18,159,6,11,536,15,160,7,13,534,17,46,653,652,658,655,636,637,642,49,639,645,644,650,44,647,626,625,627,38,621,629,628,634,41,631,164,0,540,43,1,702,697,703,699,178,582,292,429,508,179,293,427,506,580,177,581,291,428,507,578,181,295,425,504,579,182,296,426,505,577,180,294,424,503,290,184,588,435,514,185,586,433,288,512,183,587,434,289,513,584,187,431,286,510,585,188,432,287,511,583,186,430,285,509,664,666,667,671,570,606,144,496,441,568,145,494,439,604,569,605,143,495,440,602,566,140,492,437,603,567,141,493,438,601,565,142,491,436,135,576,612,502,447,574,610,500,136,445,575,611,501,134,446,608,572,498,138,443,609,573,499,139,444,607,571,497,137,442,681,678,685,688 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#164604ba66664ae7e7b126fe65d39300d84fb27e5ce614035873663e987c6567, 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 15:23:15 · history