Equation 677 Database

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Magma 66a432a9d0f0…

magma 66a432a9d0f0
Size
381
Isomorphism class hash
66a432a9d0f053f8a21b8be92207bd75209d1d051bb3e37cae6f9b19db0c1d01
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 23:17:48
Display reorder
380,146,140,150,125,130,135,313,314,312,316,317,315,166,155,161,181,170,175,200,205,211,185,190,196,3,273,4,5,6,7,238,288,233,223,228,218,38,40,48,50,296,55,73,61,67,242,25,24,252,258,248,267,277,262,97,85,90,81,280,76,121,116,291,110,100,105,351,338,365,334,356,348,361,370,377,340,149,144,154,129,134,139,326,324,325,329,327,328,169,159,164,184,174,179,204,209,214,189,194,199,16,270,15,13,14,12,235,285,230,221,226,216,35,44,46,54,299,59,70,64,65,241,10,11,250,255,245,265,276,261,99,88,94,84,284,79,124,119,294,114,104,109,354,335,369,333,359,345,364,374,379,344,148,143,153,127,133,138,303,304,305,301,300,302,168,158,163,182,172,177,203,208,213,188,193,198,1,271,17,18,0,2,236,286,231,220,225,215,36,43,45,53,298,58,74,63,69,244,33,34,254,259,249,268,279,264,95,86,92,82,282,77,120,115,290,111,101,106,350,336,367,330,358,346,362,372,378,342,147,142,152,128,131,136,311,309,310,308,306,307,167,157,162,183,173,178,202,207,212,187,192,197,30,274,29,27,28,26,239,289,234,224,229,219,39,42,49,52,297,57,72,62,68,243,31,32,251,256,246,269,275,260,98,87,93,83,283,78,123,118,293,113,103,108,353,339,368,331,357,349,363,373,376,343,145,141,151,126,132,137,321,322,323,318,319,320,165,156,160,180,171,176,201,206,210,186,191,195,23,272,22,20,21,19,237,287,232,222,227,217,37,41,47,51,295,56,71,60,66,240,8,9,253,257,247,266,278,263,96,89,91,80,281,75,122,117,292,112,102,107,352,337,366,332,355,347,360,371,375,341 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#0c1c8b18119133fb8debdb5d149d6db1ac93e4c65e1bffaee2a0311d537b261b, M = {76} 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 23:17:49 · history