Equation 677 Database

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Magma 6f38bd79b1f9…

magma 6f38bd79b1f9
Size
381
Isomorphism class hash
6f38bd79b1f9a52ad2d8a96ae991c4591464dc02f165569253b6251a286a99c9
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 23:18:40
Display reorder
380,12,153,144,142,137,307,163,181,134,174,138,154,13,145,140,308,161,179,135,175,14,152,143,141,139,306,162,180,136,173,329,155,15,176,148,166,131,168,150,170,310,156,16,177,171,146,164,132,169,151,309,157,182,178,172,147,165,133,167,149,130,128,160,158,159,129,350,364,338,349,337,336,330,351,378,365,288,268,295,260,253,322,287,251,271,244,254,269,289,296,258,320,285,249,272,245,290,267,294,259,252,321,286,250,270,243,319,273,283,246,257,293,264,298,262,242,317,274,284,247,240,255,291,265,299,263,318,275,282,248,241,256,292,266,297,261,278,276,281,279,280,277,369,370,358,335,356,334,357,355,340,377,71,96,84,124,119,302,106,88,80,114,120,97,72,85,122,301,104,86,81,115,73,95,83,123,121,300,105,87,82,113,305,98,74,116,91,109,127,111,93,9,303,99,75,117,10,89,107,125,112,94,304,100,76,118,11,90,108,126,110,92,78,79,103,101,102,77,375,346,345,374,376,347,363,362,348,379,229,216,206,196,211,313,202,200,221,237,212,217,230,204,197,311,203,198,219,238,228,218,205,195,210,312,201,199,220,239,316,186,226,208,193,7,189,231,213,236,314,187,227,209,234,194,5,190,232,214,315,188,225,207,235,192,6,191,233,215,224,222,185,183,184,223,352,367,354,331,353,368,332,366,339,333,34,52,65,47,26,325,60,42,8,70,27,50,32,66,48,323,61,43,3,68,33,51,67,49,28,324,59,41,4,69,328,55,17,23,44,62,0,37,22,39,326,53,18,24,40,45,63,2,35,20,327,54,19,25,38,46,64,1,36,21,57,58,29,30,31,56,361,373,372,344,371,342,359,341,343,360 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#0f7c66027161d31f043d2259f1b801f34900a7f6d1954571489032d4812f5629, M = {66} 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 23:18:41 · history