Equation 677 Database

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Magma 4ee0a9956709…

magma 4ee0a9956709
Size
381
Isomorphism class hash
4ee0a9956709a3a3fb283c6e2003eec2e6ced516f0da8361f2757d470b8314b8
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 23:41:15
Display reorder
380,180,281,200,223,253,261,310,311,306,307,308,309,87,88,89,84,85,86,33,34,35,30,31,32,199,219,238,258,279,299,103,104,105,106,107,102,221,251,276,296,196,216,282,182,202,224,240,262,24,25,26,27,28,29,95,90,91,92,93,94,97,99,100,96,101,98,377,335,379,347,346,375,344,334,345,361,197,297,217,237,257,277,327,328,329,324,325,326,123,124,125,120,121,122,134,135,136,137,132,133,187,207,228,254,267,287,19,20,21,22,23,18,227,244,266,286,186,206,298,198,218,239,259,278,139,140,141,142,143,138,131,126,127,128,129,130,13,15,16,12,17,14,367,352,365,333,332,372,350,353,351,360,191,291,211,232,248,271,314,315,316,317,312,313,47,42,43,44,45,46,172,173,168,169,170,171,185,205,226,243,265,285,78,79,80,81,82,83,225,242,264,284,184,204,290,190,210,231,247,270,177,178,179,174,175,176,41,36,37,38,39,40,72,74,75,77,76,73,363,358,369,343,342,370,337,359,336,374,195,295,215,236,250,275,323,318,319,320,321,322,58,59,54,55,56,57,69,70,71,66,67,68,189,209,230,246,269,289,156,157,158,159,160,161,229,245,268,288,188,208,294,194,214,235,256,274,60,61,62,63,64,65,52,53,48,49,50,51,164,166,167,163,162,165,366,341,362,356,357,373,339,340,338,378,193,293,213,234,249,273,301,300,302,303,304,305,114,115,116,117,118,119,8,9,10,11,6,7,183,203,220,241,263,283,154,155,150,151,152,153,222,252,260,280,181,201,292,192,212,233,255,272,5,1,0,2,3,4,108,109,110,111,112,113,148,144,145,147,146,149,371,331,364,355,354,368,349,330,348,376 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 = {68} 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 23:41:16 · history