Equation 677 Database

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Magma 1dfcc17a4702…

magma 1dfcc17a4702
Size
381
Isomorphism class hash
1dfcc17a47021f2aabbf16e29249d5b546894234d4a722f773198ef256a5a565
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 23:32:32
Display reorder
380,170,165,175,151,155,160,201,205,181,186,191,196,131,126,127,128,129,130,144,145,146,147,148,149,211,216,221,225,230,235,39,40,41,36,37,38,265,241,246,251,255,260,136,137,132,133,134,135,308,309,310,306,329,307,139,140,141,142,143,138,285,280,290,295,271,275,336,359,335,353,366,370,363,352,354,376,174,169,179,153,159,164,204,209,183,188,194,199,26,27,28,29,24,25,22,23,18,19,20,21,213,218,224,229,234,239,7,8,9,10,11,6,267,242,247,252,257,262,30,31,32,33,34,35,304,305,301,300,302,303,16,17,12,13,14,15,288,283,294,298,273,278,330,355,342,331,369,374,361,337,343,379,171,166,176,150,156,161,200,206,180,185,190,195,45,46,47,42,43,44,63,64,65,60,61,62,210,215,220,226,231,236,59,54,55,56,57,58,266,240,245,250,256,261,53,48,49,50,51,52,314,315,316,311,312,313,2,3,4,5,1,0,286,281,291,296,270,276,345,356,334,341,365,371,362,344,339,377,173,168,178,154,158,163,203,208,184,189,193,198,102,103,104,105,106,107,122,123,124,125,120,121,214,219,223,228,233,238,108,109,110,111,112,113,269,244,249,254,259,264,98,99,100,101,96,97,319,320,321,322,317,318,114,115,116,117,118,119,289,284,293,299,274,279,340,357,351,333,368,373,360,350,332,378,172,167,177,152,157,162,202,207,182,187,192,197,94,95,90,91,92,93,87,88,89,84,85,86,212,217,222,227,232,237,83,78,79,80,81,82,268,243,248,253,258,263,77,72,73,74,75,76,326,327,328,323,324,325,66,67,68,69,70,71,287,282,292,297,272,277,349,358,348,346,367,372,364,338,347,375 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#7eadf19d7b6e5946b2d6ebbbf061273ea953f89e2819b4463bfb57d0a1e47218, M = {75} 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 23:32:33 · history