Equation 677 Database

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Magma d8d529795db1…

magma d8d529795db1
Size
381
Isomorphism class hash
d8d529795db1ed6914d50eb52667c5320ba3267c4e77292c53af7af721cc26de
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 23:47:58
Display reorder
380,29,24,269,33,39,44,254,259,264,239,244,249,79,84,74,94,279,89,184,189,179,199,204,194,129,134,124,9,289,4,234,224,229,219,209,214,104,109,99,119,284,114,299,169,174,164,154,159,317,315,316,314,312,313,139,149,144,294,19,14,69,274,64,54,59,49,344,354,363,349,374,339,334,359,369,379,28,23,268,32,38,43,253,258,263,238,243,248,77,81,71,91,275,87,183,188,178,198,203,193,127,132,122,7,287,2,233,223,228,218,208,213,101,107,97,115,281,110,298,168,173,163,153,158,321,322,323,318,319,320,138,148,143,293,18,13,65,270,61,52,57,45,340,351,364,346,373,338,333,357,368,378,26,21,265,30,36,41,250,255,260,235,241,246,75,80,70,93,278,85,181,186,176,195,200,190,128,133,123,8,288,3,230,221,226,215,206,210,100,105,96,118,283,113,295,166,170,160,150,155,303,304,305,301,300,302,137,147,142,292,17,12,67,272,62,50,55,47,342,353,362,348,370,335,330,358,365,375,25,20,266,31,35,40,251,256,261,236,240,245,76,82,72,90,276,86,180,185,175,196,201,191,125,130,120,5,286,0,231,220,225,216,205,211,102,106,95,116,280,111,296,165,171,161,151,156,325,326,324,328,329,327,136,145,140,290,15,11,66,271,60,51,56,46,341,350,360,345,371,336,331,356,366,376,27,22,267,34,37,42,252,257,262,237,242,247,78,83,73,92,277,88,182,187,177,197,202,192,126,131,121,6,285,1,232,222,227,217,207,212,103,108,98,117,282,112,297,167,172,162,152,157,310,311,309,307,308,306,135,146,141,291,16,10,68,273,63,53,58,48,343,352,361,347,372,337,332,355,367,377 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#e6667989dcd92e07f9ac29d8b243d6a96a38fa8a609415f393f811e1aaa26c76, M = {69} 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 23:47:59 · history