Equation 677 Database

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Magma c9f4ec1c39d4…

magma c9f4ec1c39d4
Size
381
Isomorphism class hash
c9f4ec1c39d4bcd360fb3b6178f7149d13d24a20e7c63881835d9eaeb188d32c
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 23:25:16
Display reorder
380,25,20,1,5,10,15,156,161,166,171,175,151,85,61,66,71,76,81,205,181,186,191,196,200,36,40,45,50,55,31,216,221,226,231,235,211,256,261,265,241,246,251,91,96,101,105,110,115,271,276,280,285,290,295,125,135,121,140,145,130,314,316,313,317,312,315,351,349,357,370,346,335,375,360,358,369,28,23,3,8,13,18,158,163,168,173,178,153,88,63,68,73,78,83,208,183,188,193,198,203,38,43,48,53,58,33,218,223,228,233,238,213,258,263,268,243,248,253,93,98,103,108,113,118,274,278,284,289,294,299,128,138,123,143,148,133,320,322,319,323,318,321,333,353,339,371,334,350,376,363,342,368,26,21,0,6,11,16,155,160,165,170,176,150,86,60,65,70,75,80,206,180,185,190,195,201,35,41,46,51,56,30,215,220,225,230,236,210,255,260,266,240,245,250,90,95,100,106,111,116,270,275,281,286,291,296,126,136,120,141,146,131,326,328,325,329,324,327,348,347,355,373,338,343,378,362,337,366,29,24,4,9,14,19,159,164,169,174,179,154,89,64,69,74,79,84,209,184,189,194,199,204,39,44,49,54,59,34,219,224,229,234,239,214,259,264,269,244,249,254,94,99,104,109,114,119,273,279,283,288,293,298,129,139,124,144,149,134,308,310,307,311,306,309,341,345,356,374,352,344,379,364,340,367,27,22,2,7,12,17,157,162,167,172,177,152,87,62,67,72,77,82,207,182,187,192,197,202,37,42,47,52,57,32,217,222,227,232,237,212,257,262,267,242,247,252,92,97,102,107,112,117,272,277,282,287,292,297,127,137,122,142,147,132,302,304,300,305,301,303,332,354,336,372,331,330,377,361,359,365 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#4ff69c35f55aa106c20b4528e074e3f72eddedd150e00069ea529e91bc9e2010, 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 23:25:16 · history