Equation 677 Database

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Magma 2cc4b43fd7c5…

magma 2cc4b43fd7c5
Size
381
Isomorphism class hash
2cc4b43fd7c580a4265b1c8fb037ea124085c73a70701752bd5455118200c11b
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 23:42:10
Display reorder
380,30,22,24,25,26,44,27,45,23,43,138,128,130,131,132,133,134,135,139,129,184,180,182,183,185,186,187,188,189,181,230,234,232,233,235,236,237,238,239,231,326,302,303,304,301,88,78,80,81,82,83,84,85,89,79,282,284,280,283,285,286,287,288,289,281,300,352,356,338,348,351,353,369,335,339,370,34,47,46,33,32,31,36,49,48,35,144,147,146,145,143,142,141,140,149,148,194,197,196,195,193,192,191,190,199,198,247,244,246,245,243,242,241,240,249,248,310,311,313,307,308,94,97,96,95,93,92,91,90,99,98,296,294,297,295,293,292,291,290,299,298,309,378,377,375,374,373,372,371,379,376,349,5,2,4,0,38,6,39,7,37,3,106,102,104,105,100,107,108,109,110,103,157,153,155,156,152,158,159,160,161,154,203,207,205,206,202,208,209,210,211,204,314,315,316,324,317,56,52,54,55,50,57,58,59,60,53,255,257,254,256,253,258,259,260,261,250,329,337,350,361,343,342,336,360,346,345,359,21,19,41,42,16,17,18,40,28,20,126,123,124,125,127,119,120,121,122,136,178,175,176,177,179,171,172,173,174,150,225,228,226,227,229,221,222,223,224,201,306,327,323,305,328,76,73,74,75,77,69,70,71,72,86,276,278,275,277,279,271,272,273,274,252,312,355,341,367,366,340,362,347,368,357,358,14,11,13,15,29,8,9,10,12,1,117,114,101,116,118,137,111,112,113,115,168,165,151,167,169,170,162,163,164,166,215,218,200,217,219,220,212,213,214,216,318,319,320,321,322,67,64,51,66,68,87,61,62,63,65,251,268,265,267,269,270,262,263,264,266,325,365,354,334,364,363,333,332,344,331,330 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#bcdaeba3e5c42bac8c75df4a4ea039608cfd6919340934a2200e9da4b34d4d34, 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 23:42:11 · history