Equation 677 Database

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Magma 4251d25cd702…

magma 4251d25cd702
Size
381
Isomorphism class hash
4251d25cd70225df508e8b4504d6df1bb0c9bdfdff69c55b3f0cdce7ee0d8fea
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 23:32:52
Display reorder
380,285,280,290,295,270,275,328,329,324,325,326,327,216,221,226,231,236,210,27,28,29,24,25,26,150,155,160,165,170,176,240,246,251,256,261,266,1,0,2,3,4,5,14,15,16,17,12,13,19,20,21,22,23,18,196,201,206,180,186,191,6,11,10,7,8,9,364,347,375,343,338,344,370,365,335,342,288,283,293,298,274,279,312,313,314,315,316,317,219,224,229,234,239,213,147,148,149,144,145,146,153,158,163,168,173,179,243,249,254,259,264,268,123,124,125,120,121,122,134,135,136,137,132,133,139,140,141,142,143,138,199,204,209,183,189,194,126,131,130,127,128,129,363,358,379,357,355,341,374,369,333,356,286,281,291,296,271,276,308,309,310,311,306,307,215,220,225,230,235,211,108,109,110,111,112,113,151,156,161,166,171,175,241,245,250,255,260,265,107,102,103,104,105,106,94,95,90,91,92,93,101,96,97,98,99,100,195,200,205,181,185,190,116,115,114,117,118,119,360,348,376,336,352,353,371,366,354,334,289,284,294,299,273,278,304,305,301,300,302,303,218,223,228,233,238,214,78,79,80,81,82,83,154,159,164,169,174,178,244,248,253,258,263,269,77,72,73,74,75,76,64,65,60,61,62,63,71,66,67,68,69,70,198,203,208,184,188,193,86,85,84,87,88,89,361,359,378,340,349,350,373,368,351,337,287,282,292,297,272,277,323,318,319,320,321,322,217,222,227,232,237,212,50,51,52,53,48,49,152,157,162,167,172,177,242,247,252,257,262,267,46,47,42,43,44,45,35,30,31,32,33,34,39,40,41,36,37,38,197,202,207,182,187,192,55,54,59,56,57,58,362,332,377,339,330,345,372,367,346,331 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#81fb02f374018e52eb43ccfa7482c1ceb3842f71095f08d9a76873470f8f397e, M = {67} 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 23:32:53 · history