Equation 677 Database

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Magma f20f321822ff…

magma f20f321822ff
Size
381
Isomorphism class hash
f20f321822ffefc397c5d81e9b22a77b7b4e3a14f702993451d724218651f5e8
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 23:41:24
Display reorder
380,79,78,80,81,82,83,236,153,150,151,152,233,145,146,147,148,149,144,262,267,242,247,252,257,315,316,317,312,313,314,67,68,69,70,71,66,287,292,297,272,277,282,95,90,91,92,93,94,61,62,63,64,65,60,76,77,72,73,74,75,88,84,85,87,86,89,344,343,356,347,342,377,345,370,357,346,186,185,187,232,237,184,127,128,129,130,131,126,123,124,125,120,121,122,260,265,241,245,250,255,310,311,306,307,308,309,18,19,20,21,22,23,286,291,295,271,276,281,198,199,200,195,196,197,14,15,16,17,12,13,178,179,180,181,182,183,205,201,202,204,203,206,330,336,352,331,335,379,362,372,353,364,26,25,27,28,29,24,172,173,174,175,176,177,170,171,166,167,168,169,264,269,244,249,254,259,322,323,318,319,320,321,156,157,158,159,154,155,289,294,299,274,279,284,42,43,44,45,46,47,160,161,162,163,164,165,30,31,32,33,34,35,39,41,36,38,37,40,338,358,360,339,359,378,337,373,361,332,59,58,54,55,56,57,188,228,231,227,235,238,190,191,192,193,194,189,263,268,243,248,253,258,301,300,302,303,304,305,108,109,110,111,112,113,288,293,298,273,278,283,103,104,105,106,107,102,117,118,119,114,115,116,49,50,51,52,53,48,97,99,100,96,101,98,341,350,363,349,351,375,340,371,369,348,214,213,215,216,217,218,7,8,9,10,11,6,3,4,5,1,0,2,261,266,240,246,251,256,327,328,329,324,325,326,239,229,230,219,220,234,285,290,296,270,275,280,137,132,133,134,135,136,226,221,222,223,224,225,211,212,207,208,209,210,138,140,141,143,142,139,365,368,333,354,367,376,366,374,334,355 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 = {69} 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 23:41:25 · history