Equation 677 Database

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Magma a8d1e1655f08…

magma a8d1e1655f08
Size
381
Isomorphism class hash
a8d1e1655f08ea0fabf7f60d61d74f6dab6e1325857e00cc3639858d1f24c168
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:42:23
Display reorder
380,287,270,316,261,289,243,296,278,269,250,282,271,320,262,290,244,297,279,264,251,283,272,322,263,291,245,298,280,265,246,284,327,258,292,241,299,281,266,247,273,285,274,307,259,293,240,294,276,267,248,286,275,313,260,288,242,295,277,268,249,253,255,256,257,252,254,365,330,331,366,349,346,332,348,377,347,143,130,321,178,144,157,150,137,122,163,138,131,324,179,145,158,151,132,123,164,139,126,329,174,146,159,152,133,124,165,140,309,175,147,160,153,134,125,166,127,141,128,311,176,148,161,154,135,120,167,142,129,317,177,149,156,155,136,121,162,168,170,171,172,173,169,368,355,352,367,351,350,353,354,333,356,13,1,328,48,34,47,26,19,6,41,14,0,308,49,35,42,27,20,7,36,15,2,310,50,30,43,28,21,8,37,16,314,51,31,44,29,22,9,38,3,17,4,318,52,32,45,24,23,10,39,12,5,323,53,33,46,25,18,11,40,58,54,55,56,57,59,336,373,378,362,340,339,374,372,338,337,84,77,326,62,103,118,97,90,83,110,85,72,306,63,104,119,98,91,78,111,86,73,312,64,105,114,99,92,79,112,87,315,65,106,115,100,93,80,113,74,88,75,319,60,107,116,101,94,81,108,89,76,325,61,102,117,96,95,82,109,68,70,71,66,67,69,359,371,334,369,357,361,358,370,360,335,199,186,302,234,206,221,214,193,180,227,200,187,303,235,207,216,215,194,181,222,201,188,304,236,208,217,210,195,182,223,202,305,237,209,218,211,196,183,224,189,203,190,301,238,204,219,212,197,184,225,198,191,300,239,205,220,213,192,185,226,232,228,229,230,231,233,342,343,375,379,376,345,341,363,364,344 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#c1ed850353bdcc1eb7475edf09be0052f6ed9804a50fcfe49c6fc3e50f297091, M = {66} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:42:24 · history