Equation 677 Database

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Magma d7496e9930b9…

magma d7496e9930b9
Size
381
Isomorphism class hash
d7496e9930b9941d59e372b3b9cf41e5734d10e44769b7ad3e71c74ec7cc549c
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 23:30:19
Display reorder
380,325,287,297,275,292,252,245,267,248,262,327,282,298,270,293,253,241,268,250,263,258,283,299,271,288,254,240,269,251,329,259,284,247,318,294,272,289,255,242,264,260,285,246,321,295,273,290,256,243,265,286,323,296,274,291,257,244,266,249,261,278,280,281,276,277,279,370,360,369,356,334,371,333,357,358,359,328,49,5,39,59,19,7,32,16,28,319,50,1,40,54,20,8,33,17,29,24,51,0,41,55,21,9,34,12,320,25,52,13,322,2,36,56,22,10,35,26,53,14,324,3,37,57,23,11,30,48,326,4,38,58,18,6,31,15,27,47,43,44,45,46,42,336,374,362,373,377,361,335,337,372,338,311,239,189,223,185,209,197,216,200,212,306,234,190,224,180,204,192,217,201,213,214,235,191,225,181,205,193,218,202,307,215,236,203,308,186,226,182,206,194,219,210,237,198,309,187,227,183,207,195,220,238,310,188,222,184,208,196,221,199,211,231,233,228,229,230,232,363,375,343,364,340,342,379,376,339,341,314,162,176,152,172,132,120,145,129,141,315,163,177,153,173,133,121,146,130,142,143,164,178,154,168,134,122,147,131,316,138,165,126,317,179,155,169,135,123,148,139,166,127,312,174,150,170,136,124,149,167,313,175,151,171,137,125,144,128,140,160,156,157,158,159,161,353,368,352,350,367,349,366,351,354,355,300,82,90,66,86,110,98,65,107,119,302,83,91,67,87,111,99,60,102,114,115,78,92,68,88,112,100,61,103,303,116,79,104,304,93,69,89,113,101,62,117,80,105,305,94,70,84,108,96,63,81,301,95,71,85,109,97,64,106,118,74,76,77,72,73,75,365,378,330,346,331,345,344,347,332,348 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#67236894cafbadfe1162ad4049212226f9fef43fdbdc0dc282a12004458d0655, 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 23:30:20 · history