Equation 677 Database

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Magma f44bd9e03ed4…

magma f44bd9e03ed4
Size
381
Isomorphism class hash
f44bd9e03ed4f1c37d268dc8df3e56d1efb57835d8170bf1cbe0bfabaeff05da
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 23:44:46
Display reorder
380,50,49,51,52,53,48,69,70,71,66,67,68,274,278,284,289,294,299,135,136,137,132,133,134,58,59,54,55,56,57,102,103,104,105,106,107,269,244,249,254,259,264,141,142,143,138,139,140,101,96,97,98,99,100,303,302,65,60,61,304,305,62,301,63,300,64,341,379,347,346,338,340,352,373,339,353,84,89,85,86,87,88,210,211,212,213,214,215,272,277,282,287,292,297,162,163,164,165,166,167,92,93,94,95,90,91,13,14,15,16,17,12,267,240,246,251,256,261,160,161,156,157,158,159,19,20,21,22,23,18,316,315,207,208,209,317,312,204,313,205,314,206,365,377,333,332,344,364,357,374,345,356,170,169,171,172,173,168,200,201,202,203,198,199,273,279,283,288,293,298,115,116,117,118,119,114,178,179,174,175,176,177,191,186,187,188,189,190,268,243,248,253,258,263,109,110,111,112,113,108,183,184,185,180,181,182,309,308,193,194,195,310,311,196,306,197,307,192,363,378,360,361,358,362,349,372,359,348,150,155,151,152,153,154,225,226,227,222,223,224,270,275,280,285,290,295,82,83,78,79,80,81,145,146,147,148,149,144,130,131,126,127,128,129,265,241,245,252,257,262,75,76,77,72,73,74,124,125,120,121,122,123,324,323,221,216,217,325,326,218,327,219,328,220,367,376,350,351,355,366,342,370,354,343,236,235,237,238,239,234,26,27,28,29,24,25,271,276,281,286,291,296,5,1,0,2,3,4,230,231,232,233,228,229,44,45,46,47,42,43,266,242,247,250,255,260,6,7,8,9,10,11,37,38,39,40,41,36,319,322,31,32,33,318,329,34,320,35,321,30,334,375,336,337,369,335,331,371,368,330 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#d9df7de9a291eb9f8afa3ed926081c844b8ee7df4e18920313d7d7d6494810a4, 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 23:44:47 · history