Equation 677 Database

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Magma fd963842e764…

magma fd963842e764
Size
381
Isomorphism class hash
fd963842e764bd049415fe1ceb63eeafeed0d10da0d71c2feb5e91c3a5d41d9e
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 23:42:14
Display reorder
380,149,131,159,177,141,169,167,151,309,133,144,126,160,134,178,142,170,162,152,310,145,127,161,135,179,143,171,163,153,311,146,128,156,136,174,138,172,164,154,306,147,129,157,137,175,139,173,165,155,307,132,130,148,158,176,140,168,166,150,308,123,125,120,121,122,124,365,364,345,346,376,377,344,367,366,343,42,24,58,14,40,6,4,50,328,32,43,25,59,33,15,41,7,5,51,319,44,26,54,34,16,36,8,1,52,321,45,27,55,35,17,37,9,0,53,323,46,28,56,30,12,38,10,2,48,325,31,29,47,57,13,39,11,3,49,326,22,18,19,20,21,23,369,330,350,370,331,347,349,348,351,368,113,95,61,79,105,77,69,115,317,97,108,90,62,98,80,106,72,70,116,312,109,91,63,99,81,107,73,71,117,313,110,92,64,100,82,102,74,66,118,314,111,93,65,101,83,103,75,67,119,315,96,94,112,60,78,104,76,68,114,316,87,89,84,85,86,88,372,337,357,358,355,373,356,359,338,374,284,269,296,257,281,248,245,293,301,272,285,264,297,273,252,276,249,241,288,300,286,265,298,274,253,277,250,240,289,302,287,266,299,275,254,278,251,243,290,303,282,267,294,270,255,279,246,242,291,304,271,268,283,295,256,280,247,244,292,305,260,262,263,258,259,261,339,342,379,375,362,341,363,360,340,361,233,212,184,200,224,197,186,236,318,221,228,213,185,216,201,225,193,187,237,320,229,214,181,217,202,226,192,188,238,322,230,215,180,218,203,227,194,191,239,324,231,210,182,219,198,222,195,190,234,327,220,211,232,183,199,223,196,189,235,329,209,205,206,207,208,204,332,353,371,378,336,334,354,352,333,335 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#bef1fe73f4a4b6f186a10adc3b4e8a5113daf112d0dbcb5b7073730a2a52702b, 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 23:42:15 · history