Equation 677 Database

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Magma bb096f22ac77…

magma bb096f22ac77
Size
381
Isomorphism class hash
bb096f22ac7723b051e7abaf71c2a8df68a2fdcc86d67186fbc19f81f1c7aa0a
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 23:37:22
Display reorder
380,269,264,279,249,259,282,72,77,82,87,92,254,142,147,137,127,132,122,67,68,66,274,214,69,14,244,15,16,17,18,204,209,199,189,194,184,107,112,117,97,292,102,299,47,48,51,49,50,302,301,300,305,303,304,157,162,152,172,177,167,224,229,219,239,289,234,348,359,367,362,352,339,377,334,342,372,265,260,275,245,256,281,70,75,81,85,90,251,141,146,136,125,130,120,53,55,52,273,213,54,65,242,64,62,63,61,203,208,198,188,193,183,106,111,116,95,291,100,298,60,59,57,58,56,329,327,328,326,324,325,155,160,150,171,176,166,223,228,218,238,288,233,349,358,366,361,351,338,376,333,341,371,267,262,277,246,255,284,74,79,83,89,94,250,144,149,139,129,134,124,40,41,39,270,211,42,1,241,35,36,37,38,201,206,196,186,191,180,109,114,119,99,294,104,296,10,11,13,12,24,317,315,316,314,312,313,159,164,154,174,179,169,220,225,215,236,285,231,345,356,369,364,354,336,379,331,344,374,268,263,278,248,258,280,71,76,80,86,91,253,140,145,135,126,131,121,7,8,6,271,210,9,4,243,5,0,2,3,200,205,195,185,190,181,105,110,115,96,290,101,295,22,23,21,19,20,309,310,311,306,307,308,156,161,151,170,175,165,221,226,216,235,286,230,346,355,365,360,350,335,375,330,340,370,266,261,276,247,257,283,73,78,84,88,93,252,143,148,138,128,133,123,45,43,44,272,212,46,34,240,33,31,32,30,202,207,197,187,192,182,108,113,118,98,293,103,297,29,28,26,27,25,322,323,321,319,320,318,158,163,153,173,178,168,222,227,217,237,287,232,347,357,368,363,353,337,378,332,343,373 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#9acf37934a26f07a9500b1ccb24642817fa617552582595ca38f94c8a1f3c019, 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 23:37:23 · history