Equation 677 Database

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Magma 648f343e46cb…

magma 648f343e46cb
Size
381
Isomorphism class hash
648f343e46cb5b2d177f729048b1737b6a1009ebb094ec9f9d0f8b94c728d592
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 23:33:08
Display reorder
380,51,50,52,53,48,49,198,203,208,183,188,193,278,283,288,293,298,273,173,178,153,158,163,168,47,42,43,44,45,46,223,228,233,238,213,218,32,33,34,35,30,31,268,243,248,253,258,263,316,317,312,313,314,315,55,56,57,58,59,54,36,41,40,37,38,39,334,370,335,360,344,343,338,375,365,359,122,120,124,115,117,119,199,204,209,184,189,194,279,284,289,294,299,274,174,179,154,159,164,169,107,109,110,112,103,105,224,229,234,239,214,219,147,149,139,141,143,145,269,244,249,254,259,264,322,323,318,319,320,321,100,91,93,95,96,98,137,135,133,127,129,131,352,373,350,362,330,348,354,379,369,358,13,12,14,15,16,17,195,200,206,180,185,190,275,281,286,291,296,270,171,176,150,155,160,166,10,11,6,7,8,9,220,225,230,236,210,215,27,28,29,24,25,26,266,240,245,250,255,260,306,307,308,309,310,311,20,21,22,23,18,19,1,5,4,0,2,3,341,374,337,363,332,342,336,376,366,355,123,121,125,114,116,118,196,201,205,181,186,191,276,280,285,290,295,271,170,175,151,156,161,165,106,108,111,113,102,104,221,226,231,235,211,216,146,148,138,140,142,144,265,241,246,251,256,261,303,304,305,301,300,302,101,90,92,94,97,99,136,134,132,126,128,130,351,371,349,361,333,347,353,377,367,356,86,85,87,88,89,84,197,202,207,182,187,192,277,282,287,292,297,272,172,177,152,157,162,167,81,82,83,78,79,80,222,227,232,237,212,217,73,74,75,76,77,72,267,242,247,252,257,262,329,324,325,326,327,328,63,64,65,60,61,62,70,69,68,71,66,67,339,372,340,364,331,345,346,378,368,357 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 = {71} 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 23:33:09 · history