Equation 677 Database

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Magma 788e8e58338e…

magma 788e8e58338e
Size
396
Isomorphism class hash
788e8e58338e21a6bd727b3cff094a02fba883f0803b0ca1506322540cd7191d
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 395) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-02 00:27:57
Display reorder
376,359,309,353,338,263,310,265,211,264,23,267,212,266,24,273,213,272,25,279,214,278,16,350,339,348,306,351,203,249,17,256,204,18,250,257,205,19,251,258,206,20,252,259,207,21,253,260,208,307,349,352,337,308,254,261,209,22,255,262,210,168,160,161,162,163,164,165,166,167,327,159,328,329,330,362,392,383,380,379,344,38,52,188,236,39,53,189,237,40,54,190,227,41,55,182,228,42,56,183,229,43,57,363,366,313,58,184,230,44,59,185,45,231,316,333,314,367,317,334,315,232,268,271,46,233,274,277,47,343,354,364,48,234,50,186,49,235,51,187,143,149,136,137,138,139,140,141,142,144,145,146,147,148,324,390,375,385,381,373,357,358,122,281,81,98,123,282,82,99,109,283,83,100,110,280,84,101,111,287,85,102,112,288,86,103,113,290,87,104,114,88,292,105,115,89,294,106,116,90,296,107,117,91,298,108,118,92,300,95,119,93,302,96,120,94,304,97,121,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,382,395,394,377,361,320,347,15,150,79,247,1,270,80,248,2,276,70,238,3,325,318,368,4,151,71,239,5,152,72,240,6,153,73,241,7,74,154,242,8,319,360,345,9,75,155,243,10,76,156,244,11,77,157,245,12,78,158,246,13,356,326,346,14,198,202,191,192,193,194,195,196,197,199,200,201,335,336,365,393,389,386,387,371,323,340,179,0,130,218,180,269,131,219,181,275,132,220,169,60,133,221,170,61,134,222,171,62,135,223,172,63,124,224,173,125,64,341,331,321,355,342,332,322,65,225,174,126,66,226,175,127,67,215,176,128,68,216,177,129,69,217,178,26,30,31,32,33,34,35,36,37,27,28,29,311,312,372,384,388,378,391 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 396 = 1 + 5*79, 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, 5, B) with E = magma#2c4172a6e1600372fd9f11e7596b08091c7b2b9cbf8c8b848eed988794598eda, M = {75} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 79): MacNeish's product over GF(79); 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: 21.

last edited by qawbecrdtey at 2026-10-02 05:26:18 · history