Equation 677 Database

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Magma ee71c93d6cb2…

magma ee71c93d6cb2
Size
381
Isomorphism class hash
ee71c93d6cb22e6b8263aae65b25b0e2b06c406d2f3ae701bf68349866c301b1
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 23:41:03
Display reorder
380,300,301,302,303,304,305,273,123,153,183,213,243,274,124,154,184,214,244,89,84,85,86,87,88,82,83,78,79,80,81,95,90,91,92,93,94,189,219,249,279,129,159,74,75,76,77,72,73,272,122,152,182,212,242,278,128,158,188,218,248,125,185,215,275,245,155,335,334,376,336,373,340,341,362,337,372,312,317,313,314,315,316,299,149,179,209,239,269,277,127,157,187,217,247,17,12,13,14,15,16,1,0,2,3,4,5,23,18,19,20,21,22,207,237,267,297,147,177,6,7,8,9,10,11,298,148,178,208,238,268,296,146,176,206,236,266,126,186,216,276,246,156,359,358,365,339,369,332,357,370,338,367,321,320,322,323,318,319,290,140,170,202,232,260,287,137,167,198,229,257,117,118,119,114,115,116,68,69,70,71,66,67,109,110,111,112,113,108,201,231,259,289,139,169,60,61,62,63,64,65,291,141,171,203,233,261,288,138,168,200,230,258,142,199,228,292,262,172,353,354,363,349,366,351,352,360,350,378,328,327,329,324,325,326,293,143,173,190,220,263,294,144,174,204,234,264,54,55,56,57,58,59,43,44,45,46,47,42,52,53,48,49,50,51,194,224,253,283,133,163,41,36,37,38,39,40,280,130,160,191,221,250,284,134,164,195,225,254,145,205,235,295,265,175,331,342,368,355,364,346,345,361,356,374,310,309,311,306,307,308,282,132,162,193,223,252,286,136,166,197,227,256,27,28,29,24,25,26,104,105,106,107,102,103,33,34,35,30,31,32,180,210,240,270,121,151,96,97,98,99,100,101,281,131,161,192,222,251,271,120,150,181,211,241,135,196,226,285,255,165,344,343,377,348,375,330,333,371,347,379 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 = {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 23:41:04 · history