Equation 677 Database

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Magma f3921ddf31ce…

magma f3921ddf31ce
Size
381
Isomorphism class hash
f3921ddf31ced7e6a523032ee29db83ee52a2d3fde0841109296155bc4674ca9
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 23:19:41
Display reorder
380,79,121,86,309,71,106,114,99,93,113,122,80,87,310,108,66,107,115,100,94,123,81,88,306,109,67,102,116,101,95,124,82,89,317,110,68,103,117,96,90,83,125,84,307,111,69,104,118,97,91,112,120,78,85,308,70,105,119,98,92,77,73,74,75,76,72,333,366,332,331,330,334,349,350,368,367,259,271,267,319,248,287,299,279,4,291,272,260,268,321,292,246,282,294,280,5,273,261,269,322,293,250,283,295,281,1,274,262,264,324,288,249,284,296,276,0,263,275,265,326,289,251,285,297,277,2,290,270,258,266,329,247,286,298,278,3,254,256,257,252,253,255,369,370,356,377,348,355,338,357,337,339,204,217,212,327,195,229,245,225,190,237,218,205,213,328,238,196,230,240,226,187,219,206,214,318,239,197,231,241,227,191,220,207,215,320,234,193,232,242,222,188,208,221,210,323,235,192,233,243,223,186,236,216,209,211,325,194,228,244,224,189,201,203,199,198,200,202,351,353,376,375,347,336,364,352,335,354,157,136,164,312,178,144,129,143,171,151,137,158,165,313,152,179,145,130,138,172,132,159,166,314,153,174,146,131,139,173,133,160,167,315,154,175,147,126,140,168,161,134,162,316,155,176,148,127,141,169,150,135,156,163,311,177,149,128,142,170,184,180,181,182,183,185,379,365,363,346,345,362,373,374,344,378,12,54,19,301,33,39,53,61,26,46,55,13,20,300,47,34,40,48,62,27,56,14,21,302,42,35,41,49,63,28,57,15,22,303,43,30,36,50,64,29,16,58,23,304,44,31,37,51,65,24,45,59,17,18,305,32,38,52,60,25,10,6,7,8,9,11,360,361,358,372,343,371,359,340,342,341 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#1371a8eb1a0d3fdea23dd40f0b4e492a4d113abf96c87d6a9392efa8a6f14aef, 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 23:19:42 · history