Equation 677 Database

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Magma 906e6cda99f2…

magma 906e6cda99f2
Size
381
Isomorphism class hash
906e6cda99f28d612dc5e715807928b696ae9d3c7cc6fcab17afe335653c7b9c
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 23:41:50
Display reorder
380,113,112,108,109,110,111,116,117,118,119,114,115,318,319,320,321,322,317,13,14,15,16,17,12,20,21,22,23,18,19,259,264,269,244,249,254,289,294,299,274,278,284,68,69,70,71,66,67,64,65,60,61,62,63,172,173,168,169,170,171,175,177,178,174,179,176,354,345,353,337,335,373,379,361,338,346,9,8,10,11,6,7,4,5,1,0,2,3,325,326,327,328,323,324,59,54,55,56,57,58,49,50,51,52,53,48,258,263,268,243,248,253,288,293,298,273,279,283,195,196,197,192,193,194,200,201,202,203,198,199,183,184,185,180,181,182,190,186,187,189,188,191,334,331,336,344,362,372,378,363,343,364,107,106,102,103,104,105,99,100,101,96,97,98,315,316,313,312,329,314,166,167,162,163,164,165,160,161,156,157,158,159,256,261,266,240,245,250,287,292,297,272,277,282,231,232,233,228,229,230,236,237,238,239,234,235,128,129,130,131,126,127,120,122,123,125,124,121,351,330,352,360,355,371,377,356,359,369,212,211,213,214,215,210,209,204,205,206,207,208,306,307,308,309,310,311,34,35,30,31,32,33,28,29,24,25,26,27,257,262,267,242,247,251,286,291,296,271,276,281,138,139,140,141,142,143,133,134,135,136,137,132,75,76,77,72,73,74,82,78,79,81,80,83,365,357,366,340,347,374,376,348,339,333,40,39,41,36,37,38,45,46,47,42,43,44,303,304,305,301,300,302,154,155,150,151,152,153,148,149,144,145,146,147,255,260,265,241,246,252,285,290,295,270,275,280,87,88,89,84,85,86,92,93,94,95,90,91,225,226,227,222,223,224,218,220,221,217,216,219,342,349,341,358,368,370,375,367,332,350 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#b66edbbdcc18ab822aeb8c0e517cc0500614bfcd68d760a94b6b8cc01b086dc5, M = {75} 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 23:41:50 · history