Equation 677 Database

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Magma 3db010deeb56…

magma 3db010deeb56
Size
381
Isomorphism class hash
3db010deeb563cc96c9ed248e75fadb68f3478e9d38cb1e67a07e2c145e9468e
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 23:45:33
Display reorder
380,127,292,132,137,141,146,191,196,200,175,183,185,255,260,250,241,246,236,221,226,231,205,210,215,61,66,70,50,55,276,102,287,108,112,117,122,41,46,270,26,31,36,82,87,77,97,282,92,308,306,307,311,309,310,20,10,19,5,266,0,151,156,295,170,160,165,352,330,346,362,365,336,370,340,357,377,129,294,134,139,144,149,190,195,201,179,180,187,258,263,253,243,248,238,223,228,233,208,213,218,62,67,72,52,57,277,104,289,106,114,119,124,42,47,272,27,32,37,83,88,78,98,283,93,324,325,323,327,328,326,21,11,16,7,267,1,154,159,299,174,164,169,353,333,347,363,369,337,373,342,359,379,125,291,131,135,140,145,193,198,203,177,182,188,259,264,254,244,249,239,224,229,234,209,214,219,64,69,74,54,59,279,101,285,107,110,115,121,44,49,274,29,34,39,80,85,76,96,280,91,300,302,301,304,305,303,24,14,18,9,269,4,152,157,297,172,162,167,350,334,349,361,367,339,374,344,355,376,126,290,130,136,142,147,192,197,202,176,181,186,256,261,251,240,245,235,220,225,230,206,211,216,60,65,71,51,56,275,100,286,105,111,116,120,40,45,271,25,30,35,81,86,75,95,281,90,316,314,315,313,312,329,22,12,15,6,265,2,150,155,296,171,161,166,351,331,345,360,366,335,371,341,356,375,128,293,133,138,143,148,194,199,204,178,184,189,257,262,252,242,247,237,222,227,232,207,212,217,63,68,73,53,58,278,103,288,109,113,118,123,43,48,273,28,33,38,84,89,79,99,284,94,320,321,322,317,318,319,23,13,17,8,268,3,153,158,298,173,163,168,354,332,348,364,368,338,372,343,358,378 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#dba6afe67f86b36e533f777300b41b8ae8b2a840d4529c92a6cd7ab996e48d4f, M = {71} 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 23:45:34 · history