Equation 677 Database

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Magma 7c5478d4b077…

magma 7c5478d4b077
Size
381
Isomorphism class hash
7c5478d4b077866c404164dac615cd266586a407dc546cb97ee4b66cd9d45395
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 23:32:20
Display reorder
380,326,325,327,328,329,324,295,271,275,281,286,291,246,251,256,261,265,241,22,23,18,19,20,21,191,195,200,205,181,186,216,221,225,230,235,211,11,6,7,8,9,10,29,24,25,26,27,28,13,14,15,16,17,12,166,171,176,150,155,160,2,0,3,4,5,1,370,339,334,356,332,351,344,358,366,375,315,314,316,317,312,313,299,274,279,283,289,294,249,254,259,263,269,244,73,74,75,76,77,72,194,199,204,208,183,189,219,224,229,234,238,213,89,84,85,86,87,88,62,63,64,65,60,61,70,71,66,67,68,69,169,174,178,153,159,164,80,79,81,82,83,78,371,335,342,360,337,353,348,355,368,376,311,310,306,307,308,309,296,270,276,280,285,290,245,250,255,260,266,240,149,144,145,146,147,148,190,196,201,206,180,185,215,220,226,231,236,210,135,136,137,132,133,134,120,121,122,123,124,125,140,141,142,143,138,139,165,170,175,151,156,161,131,130,126,127,128,129,372,346,347,357,331,352,343,361,365,377,303,302,304,305,301,300,298,273,278,284,288,293,248,253,258,264,268,243,90,91,92,93,94,95,193,198,203,209,184,188,218,223,228,233,239,214,102,103,104,105,106,107,111,112,113,108,109,110,101,96,97,98,99,100,168,173,179,154,158,163,117,116,118,119,114,115,373,333,336,362,345,354,349,363,369,378,319,318,320,321,322,323,297,272,277,282,287,292,247,252,257,262,267,242,48,49,50,51,52,53,192,197,202,207,182,187,217,222,227,232,237,212,38,39,40,41,36,37,58,59,54,55,56,57,45,46,47,42,43,44,167,172,177,152,157,162,30,35,31,32,33,34,374,341,330,359,340,350,338,364,367,379 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 = {72} 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 23:32:21 · history