Equation 677 Database

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Magma 317e36427ef8…

magma 317e36427ef8
Size
381
Isomorphism class hash
317e36427ef872fcc030787a305b5b09232a77e554645a85e8e718819e346229
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 23:27:51
Display reorder
380,195,190,201,176,181,186,313,314,312,316,329,315,67,272,62,52,57,47,98,87,93,107,102,282,27,30,22,267,42,37,247,237,242,262,252,257,285,10,11,121,111,115,215,210,205,226,231,221,296,165,170,150,155,161,73,78,83,9,8,278,126,136,131,146,140,291,365,355,371,352,332,342,361,337,348,375,198,193,203,178,183,188,323,324,325,326,327,328,68,273,63,53,58,48,99,89,94,109,104,284,28,32,23,268,43,38,248,238,243,263,253,258,288,17,16,123,113,118,218,213,208,228,233,223,298,168,173,153,158,163,74,79,84,15,14,279,128,138,133,148,143,293,368,358,373,354,334,343,363,338,349,378,197,192,202,177,182,187,307,308,306,310,311,309,65,271,60,50,56,45,95,88,90,108,103,283,26,34,21,265,41,36,245,235,240,260,251,255,287,12,13,122,112,117,217,212,207,227,232,222,297,167,172,152,157,162,72,77,82,6,7,277,127,137,132,147,142,292,367,357,372,353,330,341,362,335,347,377,196,191,200,175,180,185,304,305,303,300,302,301,66,270,61,51,55,46,97,86,92,105,101,280,25,31,20,266,40,35,246,236,241,261,250,256,286,0,1,120,110,116,216,211,206,225,230,220,295,166,171,151,156,160,71,76,81,3,2,276,125,135,130,145,141,290,366,356,370,350,331,340,360,336,346,376,199,194,204,179,184,189,320,321,322,317,318,319,69,274,64,54,59,49,96,85,91,106,100,281,29,33,24,269,44,39,249,239,244,264,254,259,289,19,18,124,114,119,219,214,209,229,234,224,299,169,174,154,159,164,70,75,80,5,4,275,129,139,134,149,144,294,369,359,374,351,333,344,364,339,345,379 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#564914c332df918b1bab25ab6758cc0c591864f3f64c8c0ef251305010e22f83, 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 23:27:52 · history